# NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.3) Exercise 3.3﻿

## NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.3) Exercise 3.3

The NCERT textbooks are prescribed for students of every class studying in CBSE-affiliated schools. The prescribed textbook for CBSE Board students studying Maths is the NCERT book. The NCERT books were created by experts with great attention to detail and in-depth knowledge of the subject. The NCERT books are compiled in a manner that makes it easier for pupils to comprehend and grasp various ideas. NCERT textbooks have always proven to be of great assistance to students in developing their fundamental knowledge. The use of the NCERT Solutions For Class 6 Maths Chapter 3 Exercise 3.3 can help students make optimal use of the NCERT books.

### Structured theory:

The theories in the NCERT books are quite complex and structured. The way the theory is organised is incredibly advantageous to students because it makes it simpler for them to understand concepts. Students greatly benefit from the visual aids that have been provided in the NCERT textbooks because they make it simpler for them to comprehend the theory that is presented in written form. The ratio of written theory to visual representation in the NCERT book is remarkably balanced. This is crucial because if there are too many illustrations, students may not understand the theory, and if there are too many textual explanations, they might not be able to comprehend them without appropriate illustrations. To understand all the content that is enclosed in the NCERT books, students can refer to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and more.

### Simpler Questions:

The NCERT book’s questions are simple to understand and can be solved using the method taught in class.This makes it easier for the students to put the theory they have learnt into practise. It helps them understand how to use the theory they have studied to solve real-world situations. If students had been presented with challenging questions at the start of the chapter, they might not have been able to find the answers, which would be detrimental to their comprehension of the material. The simple questions provided along with each chapter in the NCERT textbooks assist students in initially gaining confidence in their ability to solve maths issues. Students can then move on to the random questions or some of the more difficult questions that appear in the later part of the chapter once they have a grasp of how to apply the theory. The easy questions aid them in applying the theory effectively to the problems. Students can solve the NCERT questions with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other such resources available on the Extramarks website.

### Building Confidence:

A student who has just learnt some theory and is given a challenging question to answer right awaywould find it an unsurmountable task. The student will undoubtedly be unable to solve it, which will demotivate them from trying to answer any other questions. Students can learn better and acquire the necessary conceptual understanding with the aid of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3.NCERT textbooks enable students to do just that with the simpler questions at first, while also giving them confidence that they can complete the arithmetic problems found in the textbook.In addition, an important feature of the NCERT book is that there is a section referred to as miscellaneous questions at the end of each chapter which contains some extremely challenging questions. The answers to the simpler questions are also given in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other tools for this chapter of Class 6 Maths.

The difficult questions in the latter part of the chapter give them an introduction to how the questions can be of various types and how they have improved their understanding of the subject to solve those questions. The difficulty of questions might be overwhelming for many students, but by practising with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3, students can gain confidence in this matter. The questions in the miscellaneous sections are frequently marked as optional, not because they are unimportant. The answers to all these can be found in tools like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and more.

### Greater Knowledge:

Students gain a deeper understanding of the ideas in the book, as well as the reasons why they are important and the precise messages they hope to express, owing to the structured format of the theories and the clarity of accompanying illustrations. How a concept can be applied to problems is demonstrated by the solved problems that follow each concept as well as the theory that is given in the book. The answers to the problems greatly assist students. Students can find the answers with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other similar resources available on the Extramarks website.

The combination of a thorough theory, a visual depiction of their theory, and working through problems aid in students’ acquisition of a little deeper comprehension of the material. Due to the quality of the NCERT books, many students—even those preparing for competitive exams—return to reference books frequently to grasp the concepts and strengthen their conceptual foundation.NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3 can help students who use NCERT books for competitive exams.Topics are presented in a structured order if students carefully read the NCERT book’s index; the curriculum is well-organised, and the order in which the topics are covered is quite systematic. A student must have knowledge of the requirements in order to learn any topic. This learning process is greatly facilitated by the NCERT book because it first provides the prerequisite knowledge needed to understand the next topic before moving on to it. Students can better understand the NCERT books with the help of tools like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. Students can gain a better understanding of subjects with the help of tools like these. Due to the fact that Maths is frequently thought of as a subject that is not simple for everyone to comprehend, without fluidity in the learning process, students may become confused or perhaps find the subject to be very difficult to learn. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students not get overwhelmed by Maths. Unstructured reference material could exacerbate the situation and make students decide they have no interest in learning Maths. This can be avoided by making use of resources like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and others that are given on the Extramarks website.

Maths is a subject that is challenging to both comprehend and put into practice. Students can better study the subject and gain a deeper understanding of it with the aid of NCERT books and resources like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. Due to the fact that the NCERT book contains so many questions, students have the opportunity to answer a lot of them and have a solidified understanding of the subject. The NCERT Maths book is crucial for students since it will boost their confidence for the examination and motivate them to study and engage with Maths. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can further help the cause.

The NCERT book undoubtedly makes a challenging and complex subject very enjoyable, which facilitates effective learning. For students who are just beginning their Maths studies, the NCERT Maths book is an obligatory read. The Class 6 Maths NCERT Book should be referred to by all students, along with the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3; even those who are not enrolled in the CBSE board. By clearing up their foundational understanding, it will assist students in achieving Maths proficiency. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are easily available and accessible for students at their convenience.

In 1969, the Indian government established the self-governing National Council for Education, Research, and Training (NCERT). The NCERT was established by the Indian government. The NCERT is anticipated to provide support and guidance to the federal and state governments with regard to initiatives and regulations aimed at enhancing academic standards. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3, along with other solutions, are available on the Extramarks website. These are provided to help with NCERT Class 6 Maths Chapter 3 Exercise 3.3 The primary objective of NCERT and the departments that constitute the organisation is to conduct, promote, and coordinate research in the field of education.The NCERT can create and publish sample textbooks, supplementary materials, newsletters, periodicals, and instructional kits specifically for students whose schools use NCERT textbooks and formats. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other resources were created with the same goals in mind.

The NCERT books include practice questions along with and at the end of each chapter for students in Class 6 as well as students in all subsequent grades. There is a deeper understanding of the topics discussed in the designated chapter in these questions. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 as well as other answers to the problems from the NCERT book are available on the Extramarks website.

Instead of trying to figure things out on their own when the students are facing challenges with regard to learning, they may refer to comprehensive and credible solutions. Students are recommended to use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 available online at Extramarks to understand how to solve problems of Maths on their own and develop their proficiency in this academic discipline. For assistance with  Class 6 Maths Chapter 3 Exercise 3.3, students could, for example, study the Class 6 Maths Chapter 3 Exercise 3.3 Solutions. The importance of comprehending the theoretical underpinnings of each chapter from the outset must be made clear to students. Students could face hindrances while finishing projects, taking part in quizzes, or performing well on final exams if they do not understand the foundational concepts of each subject. Students can carefully review the solutions in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 that the experts at Extramarks have developed. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 help students learn how to approach various question types and come up with workable answers for all of them.

Students must be made aware of the importance of understanding the theoretical foundations of each chapter, including Maths Class 6 Ex 3.3, from the start.Without understanding the foundational concepts of each subject, students may have trouble completing assignments, passing quizzes, or passing annual exams. Students have the opportunity to carefully examine the solutions compiled by highly efficient mentors when using the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. These would help students understand how to approach problems and come up with the best solutions. In order to try and understand the best possible response for the Math Class 6 Ex 3.3, students can use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. If students take this advice, they have a greater chance of passing the exam with good grades.

Subject specialists at Extramarks have created the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other solutions of a similar sort with students’ requirements in mind. As a result, they are especially appropriate for students in various classes.  Extramarks Maths mentors have created numerous solutions for Class 6th Exercise 3.3, including the NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3.On the Extramarks website, students who need assistance with the Maths Class 6 Chapter 3 Exercise 3.3, can get all of the solutions for the Class 6th Math Exercise 3.3, including the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. They can be of great help to students when they rely on them to study for their exams.

The Extramarks professionals who created the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are aware that students need a solid grounding in fundamental concepts before they can comprehend the more challenging concepts taught in higher classes.

### Access Other Exercises of Class 6 Maths Chapter 3

 Chapter 3 – Playing with Numbers Exercises Exercise 3.1 4 Questions & Solutions Exercise 3.2 12 Questions & Solutions Exercise 3.4 7 Questions & Solutions Exercise 3.5 12 Questions & Solutions Exercise 3.6 3 Questions & Solutions Exercise 3.7 11 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.3) Exercise 3.3

One of the most influential and inspiring subjects is Maths. It aids learners in developing their logical and analytical abilities. The CBSE curriculum of Maths for Class 6 covers a variety of subjects, including Fractions, Decimals, Algebra, Geometry, and Mensuration.

The Extramarks website offers significant questions for class 6 Maths that follow the most recent CBSE syllabus and the CCE (Continuous and Comprehensive Evaluation) guidelines in order to aid students in developing their maths concepts in a more effective manner. These significant questions aid students in better understanding the material and in systematic exam preparation. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can ensure that this happens.

### Access NCERT Solutions for Class 6 Maths Chapter 3- Playing with Numbers

For many students, the vastness of topics addressed in Maths could be overwhelming, but if students have a strong foundation from the start, it can be fun. Using the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3, students may better understand the basic ideas of Exercise 3.3 Class 6th. A panel of subject-matter experts at Extramarks has painstakingly developed user-friendly solutions for every subject so that students can feel less stressed when studying for exams.

In addition to reading materials like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3, students can also find other useful resources such as additional problems and past years’ papers. Students may simply access the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other resources of a similar sort on the Extramarks website. Students generally comprehend exams and their significance, but they might not fully grasp how to study without getting stressed. The Extramarks website offers NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3, allowing students to study in a stress-free manner. One tool that Extramarks experts recommend students utilise whenever possible to help them prepare for the efforts that come with exams are the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 offered on the Extramarks website for the Class 6th Maths Chapter 3 Exercise 3.3 Question 3 as well as for all the questions that are part of the chapter.

### Class 6 Maths NCERT Solutions Chapter 3 Exercise 3.3 – An overview

Each solution available on the Extramarks website provides detailed answers to questions in the NCERT book to help students compare their answers to the correct answers. Key Features of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 –

• Chapter-by-chapter homework makes life easier.
• Detailed answers to NCERT Class 6 textbook questions.
• Beautifully illustrated diagrams wherever needed, to help students understand and solve difficult Class 6 problems.
• Detailed subjective answers to questions, easy to understand and learn.
• Carefully designed by experts, the Class 6 NCERT solution fits precisely into the curriculum for all subject areas. Students have a much easier time preparing for exams when study materials are readily available.

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are provided by Extramarks, which effectively maintains the quality of teaching materials. Created by Extramarks experts and taking into account the exact needs of Class 6 students, the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 allow both subjective questions and  MCQ format questions to be answered and resolved. Students can also use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 to study specific chapters, take chapter tests, and revise chapters. This will give them comprehensive coverage of all subjects and help them find areas that they are weak in and need special attention.

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other similar resources for this chapter are beneficial for test preparation since they address all the different types of problems that can be found in the chapter’s seven exercises. These NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are produced by the subject matter specialists at Extramarks to offer the most effective ways to address the questions. These are the best study materials available to Class 6 students for achieving high marks in the Maths examination. Along with HCF and LCM, the chapter covers the themes of Multiples, Divisors, Factors, and how to detect factors and multiples. Students will more easily learn the numerous themes related to numbers by solving the textual questions in this chapter.

The Mesopotamian and other ancient civilisations are where the knowledge of Maths first appeared. It was used for trade, taxation, and scientific research, including stargazing. Many students are concerned about their Maths abilities. It is a subject that they may have a strong dislike for, mostly because they cannot comprehend the subject properly.Addressing these concerns and assisting with skill development are critical.The use of the resources available on the Extramarks website that are created by the experts of Maths like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students  developa better understanding of the subject and a good relationship with it.

There are several advantages to knowing maths in everyday life:

• It benefits a healthy brain:

A growing body of research has shown that knowledge of maths has positive effects on the brain. Crosswords, puzzles, and Maths problems are among the tough mental exercises that, according to research, can help keep a person’s brain cells healthy. Students’ problem-solving abilities enhance from early Maths instruction and improve their academic performance.  The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can be beneficial in this regard.

• Maths fosters critical thinking:

Analytical thinking refers to the process of recognising problems, gleaning crucial information from the facts, and thinking through solutions. To solve mathematical problems, students must do this. Analytical thinking may be deployed anytime there is an issue that needs to be solved, and developing it will help students deal with Maths problems that are progressively more complex. It is a highly coveted ability since it enables students to reason clearly, sort through a lot of information, and consider all sides of a situation. Students can practise this with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and many other similar resources available on the Extramarks website.

• Maths is useful for the management of finances:

Money and knowledge of Maths go hand in hand. It would be difficult to balance a budget without mathematical knowledge. The results of inadequate application of mathematical abilities include spending too much money or spending money that one does not even have.  According to highly regarded organisations such as corporations and governments, the ability to compute salaries and expenses and make future projections is a critical skill. Maths is required for students who want to manage their finances or pursue a career in financeIt is a crucial skill in life that students should learn from an early age. They can do so by being good at Maths with the help of the useful tools available on the Extramarks website, like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and many more.

• The food provision and management sectors both benefit from Maths:

Students might not be aware of how much knowledge of Maths is involved in the creation of that recipe when they are baking anything. Due to the fact that baking is a science, the proper amount of each component is calculated using Arithmetic. Although less exact than baking, cooking also utilises Maths. Maths also describes the numerous steps involved in producing safe food on a larger scale, including storage, testing, and shipping. There is Arithmetic involved in every activity, including ordering food from a restaurant, purchasing packaged goods from the supermarket, and cooking at home. Students are therefore encouraged to try to learn the subject and incorporate it into their skill set.It can be extremely beneficial not only in school but also afterward. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students practise the questions in their textbooks to help them better grasp the basic concepts.

• Maths is crucial for secure construction:

Architecture involves the application of a variety of mathematical concepts, such as Geometry and Algebra. Students who want to become architects must enrol in courses like Calculus, Trigonometry, Probability, Statistics, and other topics. These abilities are utilised to evaluate and compute designs and potential projects. To precisely measure and produce what the architect intended, contractors and construction personnel must also possess maths skills. Although extremely complex Arithmetic is rarely used in architecture, understanding the fundamentals and analytical thinking skills are essential.Students can understand the fundamentals of Maths with the help of tools like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 is the best way to get a clear understanding of what the chapter is about.

• The study of Computer Science requires knowledge of Maths:

In today’s environment, computers are becoming more significant and widespread. Not long ago, computers were massive, taking up entire rooms.Nowadays, everyone who has a smartphone carries a tiny computer around with them. The advances taking place in every sphere of society are driven by Computer Science. Students need to be familiar with a variety of maths concepts, such as Calculus, Statistics, Binary Maths, and more, in order to grasp the nuances of Computer Technology. Students can enhance their talents in fields like Coding, Database Creation, Software Development, and more by thinking “mathematically” or analytically. This can be done by practising with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other such resources available on the Extramarks website.

• Maths is utilised in the field of Medicine:

Medicine is a Science, and the majority of scientists use knowledge of Maths in their daily jobs. Professionals in medicine are not an exception. Medical experts need to gather and analyse data, which is based on numbers and statistics, to determine how well a treatment is working. Even simple tasks like writing a prescription require Maths. Based on a patient’s weight, dosage recommendations for medications exist. In order to verify that a patient is receiving the proper dosage, doctors must precisely convert measures. Students who wish to pursue education in the field of Medicine after completing their schooling also need to have a general idea and a good understanding of basic Maths. The curriculum of Maths taught to students of Class 6 can qualify as basic Maths. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students gain a good understanding of basic Maths. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students with revisions and practise the questions as many times as they wish to.

• Maths is used in every profession in some way:

There are a few different professions that obviously require  knowledge of Maths, but in actuality, knowledge of Maths is used in all professions. While some are devoted to maths and analytical thinking, some employ it more than others. Even if the line of work appears to be completely unrelated to Arithmetic, students will still encounter themes of Maths in the form of budgeting, making invoices, determining raises etc. As a result, having a solid knowledge base in the subject is criticalStudents can develop a good knowledge base with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other such resources.

• Maths is a universal language:

The term “universal language” is frequently used to describe Maths. Maths concepts and foundations are universal. 2 plus 2 will always equal 4 no matter where the student is from. Geometrical forms such as Circles are unchanging. Various units of measurement and different symbols for numbers may exist, but when translated, they all come out to have the same meaning.he application of maths knowledge is unavoidable and thus extremely important.Therefore students are advised to make use of tools like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 so as to optimally utilise the information available on the Extramarks website provided by the experts of Maths. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can really help students not only practise the questions in the NCERT book but also understand the themes covered in Chapter 3 of Class 6 Maths.

• Maths enables students to comprehend the cosmos:

Discoveries facilitated by Maths have taught a lot about how the universe functions. The understanding of space and time has changed as a result of Einstein’s development of the theory of relativity. The mathematical basis for researching nuclear energy was also provided by the theories. Many people think that Maths is the language of the cosmos as well as  a universal language. Therefore, students who plan to continue their studies in this field are recommended to use tools like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 that can help them understand the foundational themes of Maths from an early age.

### Playing with Numbers Exercise 3.3 – All Questions

The Class 6th Maths Chapter 3 Exercise 3.3 Question 3 is part of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are the solutions to the questions provided in the NCERT textbook for Class 6 Chapter 3 of Maths. This chapter is about ‘Playing With Numbers’. When students read this chapter, they might arrange the numbers, learn the BODMAS rule, determine whether a particular number is a factor or multiple of another number, and comprehend the characteristics of factors and multiples. Additionally, the concept of co-prime numbers and prime factorisation, determining HCF and LCM, simplifying brackets, multiples, and factors, and utilising an index or exponent for a number are all things that students are taught in this chapter. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students better grasp the concepts taught in this chapter.

When compared to procedures involving just two numbers, solving an arithmetic expression that includes numerous operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how students work out an expression with brackets and several operations, as well as how to make a bracket simpler, is a pertinent question.

• BODMAS RULE:

For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, is also known as BODMAS sometimes. Students can better understand and practice this topic that’s part of Chapter 3 of Class 6 Maths, with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and the solutions to all the other exercises of Chapter 3.

• Rule Explanation for BODMAS:

It illustrates the steps that need to be taken in order to solve an expression. The BODMAS rule states that if an expression involves brackets such as () or [], then students must first solve or simplify the bracket before moving on to the left-to-right operations of division, multiplication, addition, and subtraction. The incorrect solution will be obtained by resolving the issue in the incorrect order. When an expression has many operators, the BODMAS rule can be used. In this instance, students must first simplify the words inside the brackets, from the innermost to the outermost brackets [()], as well as any roots or exponents that may be present. then carry out the division or multiplication operation, going from left to right. Students can sometimes find this topic to be a little confusing. It is a new concept for them and, hence, challenging to many. The use of  NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 to practise the questions in the chapter, can help students understand the topic covered in the chapter better.

The other topic taught in the third chapter of Class 6 Maths is HCF and LCM. The highest number that divides each of the given numbers without leaving a remainder is known as the Highest Common Factor (HCF) of two or more given numbers. The smallest common multiple of two or more numbers is known as the Least Common Multiple (LCM). Maths concepts like HCF and LCM are crucial because they enable students to deal with grouping and sharing issues that arise on a daily basis. The highest common factor (HCF) between two or more provided numbers is characterised as being present. The phrase “Greatest Common Divisor” is another name for it (GCD). For instance, the HCF of 24 and 36 is 12, since 12 is the biggest number that can completely divide both numbers. The smallest number that is a common multiple of the given numbers is known as the Least Common Multiple (LCM) of two or more numbers. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students practise questions based on this topic and therefore master the topic through revision and practice. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 allow students to access the answers to their textbook questions whenever they need to. This makes it highly accessible and useful for students to go through the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other such tools for quick revision before the examinations.

### Extramarks– Your Online Companion for Exam Preparations

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are just one set of solutions available on the Extramarks website. The website has many useful reference materials, like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3.  The NCERT Solutions for Class 6 Maths, Chapter 3, Exercise 3.3, are created by math experts and are thus a reliable source for students to rely on.The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are focused only on the questions that are given in Exercise 3.3 of Chapter 3 of Class 6 Maths. The NCERT books have different exercises in each chapter. This is done to make the learning process easier and less confusing.

When students make use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3, which are divided by exercise-wise format similar to the NCERT book; they get to focus on one topic or several topics at a time. This can make it easier for students to not get confused. The availability of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 makes the process of accessing them convenient and easy. Students who wish the access the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 have to simply visit the Extramarks website. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 are available on the Extramarks mobile application as well. This means the students can get access to it through their phones too.

Class 6 is a crucial class as this is the first step the students take towards the secondary section of their school education.As a result, many students may find the topics covered in the Class 6 curriculum to be extremely difficult. These topics are new and more complex than what the students study in Class 5 or other classes in the primary section. The use of  tools like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 is recommended by the experts at Extramarks. Students who make use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other such tools have a higher chance of forming a strong knowledge base in the subject they are studying. A strong base is absolutely necessary to be able to perform well in not just the current class the students are in but also in senior classes. Students can achieve a stronger understanding of fundamental concepts with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other similar reference materials available on the Extramarks website.

When students do not get the chance or avoid forming a good knowledge base with regard to any topic or subject, they have the chance of developing inhibitions related to that topic or subject. This happens because they are unable to fully grasp the topic and solve questions based on it. The experts at Extramarks recommend the use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 so as to avoid \ situations like these when students develop inhibitions about a particular topic or the entire subject.

Q.1 Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10 ; by 11 (say, yes or no):

 Numbers Divisible by 2 3 4 5 6 8 9 10 11 128 990 1586 275 6686 639210 429714 2856 3060 406839

Ans.

 Numbers Divisible by 2 3 4 5 6 8 9 10 11 128 Yes No Yes No No Yes No No No 990 Yes Yes No Yes Yes No Yes Yes Yes 1586 Yes No No No No No No No No 275 No No No Yes No No No No Yes 6686 Yes No No No No No No No No 639210 Yes Yes No Yes Yes No No Yes Yes 429714 Yes Yes No No Yes No Yes No No 2856 Yes Yes Yes No Yes Yes No Yes No 3060 Yes Yes Yes Yes Yes No Yes Yes No 406839 No Yes No No No No No No No

Q.2 Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:
(a) 572 (b) 726352 (c) 5500 (d) 6000
(e) 12159 (f) 14560 (g) 21084 (h) 31795072
(i) 1700 (j) 2150

Ans.

(a) 572
Since, last two digits i.e., 72 is divisible by 4.
So, 572 is divisible by 4.
572 is not divisible by 8.

(b) 726352
Since, last two digits i.e., 52 is divisible by 4.
So, 726352 is divisible by 4.
Last three digits 352 is divisible by 8, so given number is divisible by 8.

(c) 5500
Since, last two digits i.e., 00 is divisible by 4.
So, 5500 is divisible by 4.
Last three digits 500 is not divisible by 8, so given number is not divisible by 8.

(d) 6000
Since, last two digits i.e., 00 is divisible by 4.
So, 6000 is divisible by 4.
Last three digits 000 is divisible by 8, so given number is divisible by 8.

(e) 12159
Since, last two digits i.e., 59 is not divisible by 4.
So, 12159 are not divisible by 4.
Last three digits 159 are not divisible by 8. So 12159 is not divisible by 8.

(f) 14560
Since, last two digits i.e., 60 are divisible by 4.
So, 14560 is divisible by 4.
Last three digits 560 are divisible by 8. So 14560 is divisible by 8.

(g) 21084
Since, last two digits i.e., 84 are divisible by 4.
So, 21084 is divisible by 4.
Last three digits 084 are not divisible by 8. So 21084 is not divisible by 8.

(h) 31795072
Since, last two digits i.e., 72 are divisible by 4.
So, 31795072 is divisible by 4.
Last three digits 072 are divisible by 8. So 31795072 is divisible by 8.

(i) 1700
Since, last two digits i.e., 00 are divisible by 4.
So, 1700 is divisible by 4.
Last three digits 700 are not divisible by 8. So 1700 is not divisible by 8.

(j) 2150
Since, last two digits i.e., 50 are not divisible by 4. So, 2150 is not divisible by 4.
Last three digits 150 are not divisible by 8. So 2150 is not divisible by 8.

Q.3 Using divisibility tests, determine which of following numbers are divisible by 6:
(a) 297144 (b) 1258 (c) 4335 (d) 61233
(e) 901352 (f) 438750 (g) 1790184 (h) 12583
(i) 639210 (j) 17852

Ans.

(a) 297144
Since, the last digit is 4 which is divisible by 2.
So, 297144 is divisible by 2.
2 + 9 + 7 + 1 + 4 + 4 = 27 is divisible by 3.
So, 297144 is divisible by 3.
Since, 297144 is divisible by 2 and 3.
So, 297144 is divisible by 6.

(b) 1258
Since, the last digit is 58 which is divisible by 2.
So, 1258 is divisible by 2.
1 + 2 + 5 + 8 = 16 is not divisible by 3.
So, 1258 is not divisible by 3.
Since, 1258 is divisible by 2 but not by 3.
So,1258 is not divisible by 6.

(c) 4335
Since, the last digit is 35 which are not divisible by 2.
So, 4335 is not divisible by 2.
4 + 3 + 3 + 5 = 15 is divisible by 3.
So, 1258 is divisible by 3.
Since, 1258 is divisible by 3 but not by 2.
So, 1258 is not divisible by 6.

(d) 61233
Since, the last digit is 33 which are not divisible by 2.
So, 61233 is not divisible by 2.
6 + 1 + 2 + 3 + 3 = 15 is divisible by 3.
So, 61233 is divisible by 3.
Since, 61233 is divisible by 3 but not by 2.
So, 61233 is not divisible by 6.

(e) 901352
Since, the last digit is 52 which are divisible by 2.
So, 901352 is divisible by 2.
9 + 0 + 1 + 3 + 5 + 2 = 20 is not divisible by 3.
So, 901352 is not divisible by 3.
Since, 901352 is divisible by 2 but not by 3. So, 901352 is not divisible by 6.

(f) 438750
Since, the last digit is 50 which are divisible by 2.
So, 438750 is divisible by 2.
4 + 3 + 8 + 7 + 5 + 0 = 27 is divisible by 3.
So, 438750 is divisible by 3.
Since, 438750 is divisible by 2 and by 3. So, 901352 is divisible by 6.

(g) 1790184
Since, the last digit is 84 which are divisible by 2.
So, 1790184 is divisible by 2.
1 + 7 + 9 + 0 + 1 + 8 + 4 = 30 is divisible by 3.
So, 1790184 is divisible by 3.
Since, 1790184 is divisible by 2 and by 3. So, 1790184 is divisible by 6.

(h) 12583
Since, the last digit is 83 which are not divisible by 2.
So, 12583 is not divisible by 2.
1 + 2 + 5 + 8 + 3 = 19 is not divisible by 3.
So, 12583 is divisible by 3.
Since, 12583 is divisible by 2 and by 3. So,12583 is divisible by 6.

Q.4 Using divisibility tests, determine which of the following numbers are divisible by 11:
(a) 5445 (b) 10824
(c) 7138965 (d) 70169308
(e) 10000001 (f) 901153

Ans.

 Number Sum of the digits ( at odd places ) from the right Sum of the digits ( at even places ) from the right Difference ( a ) 5445 5 + 4 = 9 4 + 5 = 9 9 − 9 = 0 ( b ) 1 0 824 4 + 8 + 1 = 13 2 + 0 = 2 13 − 2 = 11 ( c ) 7138965 5 + 9 + 3 + 7 = 24 6 + 8 + 1 = 15 24 − 15 = 9 ( d ) 70169308 8 + 3 + 6 + 0 = 17 0 + 9 + 1 + 7 = 17 17 − 17 = 0 ( e ) 10000001 1 + 0 + 0 +0 = 1 0 + 0 + 0 + 1 = 1 1 − 1 = 0 ( f ) 901153 3 + 1 + 0 = 4 5 + 1 + 9 = 15 15 − 4 = 11

If the difference is divisible by 11, the number is divisible by 11 . Here, 7138965 is not divisible by 11 .
Numbers (a) 5445 (b) 10824 (d) 70169308 (e) 10000001 and (f) 901153 are divisible by 11 .

Q.5 Write the smallest digit and the greatest digit in the blank space of each of the following numbers so that the number formed is divisible by 3 :

1. __ 6724
2. 4765 __ 2

Ans.

1.
The sum of given digits = 6 + 7 + 2 + 4 = 19
On adding 2 in 19, we get 21 which is divisible by 3. Therefore, the number formed by using the smallest digit is 26724.
On adding 8 in 19, we get 27 which is divisible by 3. Therefore, the number formed by using the greatest digit is 86724.

2.
The sum of given digits = 4 + 7 + 6 + 5 + 2 = 24
On adding 0 in 24, we get 24 which is divisible by 3. Therefore, the number formed by using the smallest digit is 476502.
On adding 9 in 24, we get 33 which is divisible by 3. Therefore, the number formed by using the greatest digit is 476592.

Q.6 Write a digit in the blank space of each of the following numbers so that the number formed is divisible by 11 :

(a) 92 __ 389

(b) 8 __ 9484

Ans.

(a) 92 __ 389
The sum of digits at odd places from right
= 9 + 3 + 2
= 14
The sum of remaining digits from right
= 8 + 9
= 17
The difference = 17 – 14 = 3
The difference will be divisible by 11, if 8 is added in 3. Therefore, the missing digit is 8.

(b) 8 __ 9484
The sum of digits at even places from right
= 8 + 9 + 8
= 25
The sum of remaining digits at odd positions from right = 4 + 4
= 8
The difference = 8 – 25
= – 17
The difference will be divisible by 11, if 6 is added in – 17. Therefore, the missing digit is 6.
Therefore, the number is 869484.

## 1. What does Chapter 3 of Class 6 Maths teach about the properties of factors?

Chapter 3 of Class 6 Maths talks about the properties of factors and there are certain facts that are established –

• 1 is a factor of all numbers, according to the properties of factors.
• Every number has a multiplier of one.
• Each of a number’s factors is a direct divisor of the original number.
• A given integer has a finite number of factors

Students are advised to practice the questions that revolve around topics that are taught in Chapter 3 of Class 6 Maths with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other such resources created specifically for the curriculum of Chapter 3.

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students understand all these topics and more. Students should make the most of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 for their benefit.

## 2. What kinds of numbers are covered in Chapter 3 of the Class 6 Maths according to the most recent CBSE curriculum?

According to the most recent CBSE syllabus, the types of numbers covered in Chapter 3 of Class 6 Maths are:

• Prime Numbers
• Even Numbers
• Odd Numbers
• Whole Numbers
• Natural Numbers
• Composite Numbers

Students can understand all these with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other solutions based on Chapter 3 of Class 6 Maths.

Prime numbers –

Those greater than one are known as prime numbers. They simply have two variables: the number itself and factor 1. This indicates that these numbers cannot be divided without leaving a remainder by any number other than 1 and the number itself. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 along with the many other tools that are available for the students on the Extramarks website, can be useful in understanding this topic.

Even numbers –

An even number is one that can be divided by two and leaves a remainder of zero. Even numbers include 2, 4, 6, 8, 10, and so on. The  NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can help students better understand even numbers and related concepts.

Odd numbers –

A number that cannot be divided by two is said to be odd. When an odd number is present, the remainder is always “1”. 11 is an example of an odd number. Use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and many other tools on the Extramarks website based on this chapter can help students know more about this topic.

Whole numbers –

Whole numbers are defined as natural numbers plus zero (0). To better understand this, it is recommended that students use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and more such tools available on the Extramarks website.

Natural numbers –

It is important to understand this theme in-depth and that can be done with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and other similar tools made for Chapter 3 of Class 6 Maths.

Composite numbers –

The majority of numbers, known as composite numbers, include more than two factors. To better understand this, it is recommended to use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and similar academic content made for Chapter 3.

The use of the resources available on the Extramarks website created proficient instructors of Maths like the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 and similar resources for other exercises as well can really help students practice different questions based on these topics. The practice done with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 can really help the students in grasping the concepts in the chapter easily. Students can use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 not only for practice but also to take help when completing their homework. The use of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.3 facilitates learning.