NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.6) Exercise 3.6
NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.6) Exercise 3.6
It is a common belief that Maths is a difficult subject. However, this is an overstatement. Mastering the subject just requires some practise and focus. Students should practise as much as possible to master the subject. Students should keep their heads clear when tackling a difficult Math problem.Before taking any exam, they should try to be confident. It takes practise to become perfect. When students are at ease and confident, they will be more capable of handling any given challenge.
Many students find Maths to be difficult, so for them, a career in Maths or any other field requiring this subject may be completely out of the question. Students find Maths to be increasingly complex. Therefore, the answer to the question of how to perform well with regard to Maths is as simple as learning from errors. Their chances of receiving good marks will rise because they can make sure not to make those errors again in their paper.
A notebook comprising all most essential formulas is one of the essential resources students can have. The key to success in Maths is understanding and applying the formulas. Therefore, students require a tool to make sure that all the formulas are at their fingertips. Making a notebook with all the formulas written appropriately achieves this goal.It assists students in reviewing and recapitulating what they have already learned, as well as keeping track of all the formulas they require in one place.. The formulas students study for all levels can be written down in a notebook.
Students ought to know the subjects that will make up the majority of the exams before they begin their exam preparation. The entire syllabus should be practised, but they should start with the chapters that carry the most weight before moving on to the others. This will give them more confidence for the exam and help them score higher.
Maths is a subject that builds on itself; understanding more complex concepts in higher classes is only possible if students have a firm grasp of the fundamental ideas.If students are having difficulty understanding a particular topic, they should reread the previous pages of the book and practise the ideas there.Moreover, students are advised to gradually move towards solving questions of increasing difficulty. This would help students stay motivated, understand the concept, and pace themselves as they practice. Students should seek assistance from teachers or peers if they need help determining the level of the question difficulty. Students can also use reference materials that contain questions organised by difficulty level.This approach will also assist students in determining their areas of strength as well as their areas of weakness.
On the Extramarks website, students can download the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. The knowledgeable mentors of Extramarks, who have years of experience instructing this course, have created all of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. These NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are logically organised using a stepbystep process to ensure clarity and comprehension. They will help students ace the test with the questions they have prepared.
Extensive practice will ensure that students approach the exam with confidence. If students have access to the NCERT solutions for Class 6 Science, Maths, English, Hindi, and other subjects, studying these subjects will be much simpler. If students need assistance with Class 6th Exercise 3.6, they can consult the NCERT solutions available on the Extramarks website. When using NCERT solutions, students can easily complete Class 6th Math Exercise 3.6.
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 3.3 
6 Questions & Solutions

Exercise 3.4 
7 Questions & Solutions

Exercise 3.5 
12 Questions & Solutions

Exercise 3.7 
11 Questions & Solutions

NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.6) Exercise 3.6
With the aid of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6, students will gain knowledge of the prime factorisation technique covered in the preceding exercise by using different methods to determine the HCF of two numbers. As the ideas covered in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are frequently used in the theorems of advanced Maths, they serveas a foundation for higher classes.
The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 have questions that need to be answered in detail and stepbystep. By using the prime factorisation technique to identify the common factors of two or more numbers, students can further explore the ideas behind HCF. Students can solve their questions with the help of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are quality reference materials to practice and understand concepts.
Access NCERT Solutions for Class 6 Maths Chapter 3 – Playing with Numbers
Students can learn more about multiples, divisors, factors, and the recognition of multiples and factors by using the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 based on Playing With Numbers. Whole numbers and natural numbers were covered in two chapters. This chapter will advance students’ understanding by teaching them what factors and multiples of a number mean. Activities relating to these ideas are included in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6, which make learning incredibly simple.
Students can determine a number’s factors using various strategies with the help of the exercise questions. Additionally, they will be able to comprehend how to use these ideas in their everyday lives. There are 7 exercises in Chapter 3 of Playing with Numbers. Students can take help from the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 to understand the chapter deeply. Moreover, students can also use NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 for exam preparation. One of the key ideas covered in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 is finding a number’s factors stepbystep. Students must answer every question in this NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 in order to gain a firm understanding of the concepts. Regularly practising with NCERT Solutions for Class 6 Maths, Chapter 3 Exercise 3.6, is the best way to develop concrete knowledge with regard to fundamental concepts of मैथ्स। As a result, students should periodically check the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 and review all the questions. Students use numerals to count things; they are everywhere, including the time, date, year, and weather.Currency counting, measurement, reading, page numbers, locks, and television channel selection are all examples of how numbers are used. When building structures and roads, engineers use numbers in their calculations. Doctors use them to administer medication and check blood counts. The knowledge of numbers is crucial for all to thoroughly study numbers because they have such a wide range of applications. Multiples, divisors, factors, multiple identification, and factors are the subjects covered in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6.
Students will also learn how to use the factors to determine whether a number is prime or composite. Students will also investigate the factors method’s application to HCF and LCM determination.In Class 6 Maths Chapter 3, “Playing with Numbers,” there are 52 questions, 30 of which are simple shortanswer sums, 15 are longanswer problems, and the remaining 7 are complex problems.. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 will guide students in solving the questions. Students can also download the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 offline to practise according to the scheduled time. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are created in easy language to understand the concepts. Students can get the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 from the Extramarks mobile application.
The resources needed to perform better on board exams are available on the Extramarks website and mobile application. Additionally, students should frequently refer to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 as they study for the Maths exams. Students can better understand the concepts covered in the textbook with the assistance of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. Highly experienced teachers prepare these solutions following the most recent CBSE Syllabus. Students’ confidence is boosted as they study for their final exams owing to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. Students can also quickly complete the Maths review exercise and assess their responses with the aid of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. Additionally, students in Class 6 can understand the proper way to respond to Maths questions with the help of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6.
The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 based on Playing with Numbers are beneficial for exam preparation as they address all of the questions found in the seven exercises in this chapter. The subject matter experts of Extramarks produced these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 at Extramarks to offer the most effective ways to address Maths problems. These are the best study materials available to Class 6 students of the CBSE Board for achieving high marks in the Maths examination. Along with HCF and LCM, the chapter also covers the ideas of multiples, divisors, and factors and how to recognise them. Students will more easily understand the various numbersrelated topics by solving NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6.
Chapter 3: Playing with Numbers
The chapter discusses factors, multiples, prime numbers, composite numbers, tests for number divisibility, common factors, common multiples, prime factorisation, highest common factor, lowest common multiple, and some issues involving LCM and HCF. In order to make it easier for students to distinguish between the topics, these topics have been divided into seven exercises.
The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 can be used as reference material by students who are having difficulty with Chapter 3. Students can easily download and complete the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 on the Extramarks website and mobile application.
The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are even available for offline download in PDF format for students. Many students strive to attain excellence in various competitive examinations, so they are suggested to print the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 offline and study in accordance with their schedules.
3.1 Introduction
The basis of Maths is numbers. Maths begins with numbers. In this chapter, titled “Playing with Numbers,” students would explore the various properties of numbers anf their types, including Prime Numbers, Composite Numbers, Factors and Multiples, HCF, LCM, etc. This chapter’s first section provides a brief overview of the topics that will be covered. Students learn to quickly count larger blocks of items using multiplication rather than addition. The entire chapter is built around this section. The basic ideas and characteristics of numbers are covered. Students will discover, for instance, that any number is a multiple of itself. They will go into great detail about this idea. They will discover the reasons behind it rather than simply retaining it. Extramarks provides solutions to exercise questions included in a PDF file to help with this. The practice questions can be attempted first by the students. They can then check to see if their answers were correct by looking at NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6.
3.2 Factors and Multiples
Students gain indepth knowledge of factors and multiples in this section. They will develop the ability to distinguish between the two terms. When attempting to answer questions later in the chapter, students could frequently become confused between the two. To prevent students from getting confused with regard to the two ideas, Extramarks provides NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. They will become familiar with the fundamental attributes of factors and multiples. They will discover, for instance, that a given number has a finite number of factors. However, there are an infinite number of variations on a given number.
3.3 Prime and Composite Number
Definitions of prime and composite numbers are given at the start of this section. A number that can only be divided by one is said to be a prime number. Students will be presented with truefalse questions in this section. They can refer to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 if they believe their response to this question was incorrect. Class 6 Maths Chapter 3 Exercise 3.6 Solution is accompanied by many practice questions covering all the topics.
3.4 Tests for Divisibility of Numbers
Every student has mastered various mathematical tables and the themes of multiplication and division. They are proficient in threedigit multiplication and long division. They will learn easy tricks and tips for multiplication and division in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. This section expands on the knowledge that students gained in earlier lessons. The first task for the students is to complete the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 by applying the divisibility rule from their textbooks. By manually dividing the numbers, they will then verify their conclusion. Students will benefit from practising the rules and reviewing their division and multiplication abilities. Students will start recognising patterns in the divisibility rules once they have mastered them. They can learn additional advice and techniques as a result. Additionally, they will learn the craft of reasoning. This helps students later in the course when they start learning concepts related to Geometry.
3.5 Common Factors and Common Multiples
Students are introduced to the ideas of common factors and common multiples in Section 3.5 of the chapter. They are first taught to distinguish between factors and multiples. The solutions prepared by Extramarks explain these concepts to students by including answers to multiplechoice and True/False questions which are provided in the exercise. A question is given to the class, and they are asked to distinguish between factors and multiples. To doublecheck their answers, they can refer to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6.
Students will then be required to write down the multiples of that number and carefully note any common factors or multiples. 6 has the factors 1, 2, 3, and 6, for instance, and the multiples of 6 are 30 and 6.
3.6 Some More Divisibility Rules
Students will learn more rules for divisibility in this section. The purpose of this section is to build on the information presented in section 3.4. Students will learn, for instance, that if a number is divisible by another number, it is also divisible by each of the other number’s factors. Students can better understand the divisibility rules as a result of this. Students can take help from the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 to understand this section. Prime numbers are discussed once more in this section. A different rule will be applied by the students using the definition of prime numbers. If two coprime numbers can divide a given number, then the product of the two coprime numbers can also divide the given number. The majority of students would not have any trouble understanding this rule. It provides information on how students can determine a rule based on data. Another rule that is introduced in this section states that if two numbers are divisible by a certain number, then their sum must also be divisible by that same number.
3.7 Prime Factorisation
Students study the idea of factorisation using prime numbers in section 3.7 of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. In this section, they will put all the previously learned concepts to use. In this section, Extramarks provides questions for comprehensive practice. The academic content provided by Extramarks ensures that as the students complete the new exercises, they are also reviewing the prior ideas. Preparing for the exam helps the students make their practise flawless.
The NCERT Maths textbook’s structure and procedures are followed by the Extramarks PDF. This ensures that every question is appropriate for the student’s level and that none is outside the parameters of the syllabus.
Extramarks provides academic reference materials for thorough preparation that are completely in line with the syllabus and exam format. This will save time for teachers, parents, and students by eliminating the need for them to look for practise materials elsewhere. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are the best study material for students to understand the concepts.
3.8 Highest Common Factor
The idea of the greatest or highest common factor (GCF or HCF) is introduced in Section 3.8. Students use their understanding of factorisation and divisibility rules to identify the greatest common factor. Extramarks has also included questions in this section that call for theorising and knowledge application rather than the straightforward execution of conventional steps. A common question, for example, is to find the greatest common divisor of two consecutive odd numbers. It calls for indepth reasoning and higherorder thinking. Such inquiries further strengthen students’ conceptual understanding.They make sure they fully comprehend the definition. Another question format asks students to make educated guesses about the numbers after being given the GCF of the numbers. A question like this, which asks the students to go back and complete the steps, aids in establishing the idea in their understanding.
3.9 Lowest Common Multiple
The lowest common multiple (LCM) of two numbers is the subject of this section. Extramarks provides NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 to enable students to put this idea into practice. The textbook provides stepbystep instructions for how to approach this question. Extramarks ensures that each student follows the same process to arrive at the solution. Students must have a firm grasp of the principles of factorisation and prime numbers before moving on to this section. They will have trouble answering these questions if the students are not proficient in those subjects. Further, NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are also provided for assistance with this section.
At the conclusion of this section, the NCERT textbooks also present some thoughtprovoking queries. In these questions, students are given an array of numbers, and they must determine the GCF, LCM, factors, and multiples of those numbers. Students must complete this as they would a crossword puzzle. Such questions are popular among students because they allow them to be creative by filling in the blanks with different coloured pencils.3.10 Some problems of HCF and LCM
The most significant portion of this chapter is this one. The chapter includes realworld examples that enable students to put all the theories they have learned to use. In this section, the NCERT textbooks ensure that the exercises apply to the students’ everyday lives.
Students will learn how to put their theoretical knowledge into practice.
The search for two sets of numbers with the same LCM is a different kind of problem. Students must apply the rules of divisibility to this question and eliminate any impractical options. They will then go on to determine the LCM of the options that are still available. Students can learn how to approach exam questions by attempting these kinds of questions, and they can also save time by skipping unnecessary steps. NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 also introduces students to the concepts of LCM and GCF for multiple numbers.Students will perfectly master the skills owing to such diligent practise with the aid of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. Furthermore, these types of questions ensure that students are at ease when taking the exam.About Extramarks
Extramarks is an online learning platform that focuses on preschool, K–12, higher education, and Test Preprepartion segments through the skilful blending of pedagogy and technology to enable learning anywhere, at any time. With the Extramarks Learning App’s interactive video modules, Extramarks guarantees conceptbased learning. These modules were created by a panel of inhouse, highly qualified subject matter experts who provide 360degree coverage of every concept. This creates the opportunity for immersive online learning, which ensures deeper retention and comprehension while preparing for exams.
Extramarks’ goal is to enable students to learn in the most effective ways at their own pace and in the convenience of their own homes through online learning solutions.They want to increase interactivity while incorporating better graphics and visuals to entice learners to study.
For its endtoend learning solutions that link students and teachers on the online learning platform, Extramarks has earned the trust of 10,000+ top schools in India. As their dependable learning partner, Extramarks encourages students to embrace a constantly changing world to prepare them for the future. Leading educators who are also experts in their fields, can impart knowledge to students. Their learning modules with rich media go into great detail about each lesson. Extramarks constantly emphasises the significance of concepts, details, and quick learning to help students gradually improve their grades and learning outcomes.
The Extramarks Learning App offers chapterbychapter worksheets, engaging activities, an endless supply of practice questions, and more to help students fully understand all subjects and topics. Students can evaluate their knowledge using adaptive tests with increasing levels of difficulty, multiple choice questions, and mock exams to build an upward learning graph. Extramarks keeps track of students’ performance on the learning platform and produces reports and analyses to help them maximise their learning experience. This performance analysis identifies students’ strong and weak areas so they can strategically plan their studies. Extramarks injects life into the monotony of textbook renderings of concepts by adding graphics and animations. Understanding and memory retention during online learning is incredibly simple, owing to the Extramarks website’s 2D and 3D animation expertise. Extramarks creates online learning programs for today’s students. They want to facilitate the learning process of students, so they use Gamified Learning Experiences to make learning engaging and interactive.
Why Extramarks?
Extramarks uses technology to aid students in exam preparation. The methods of learning must also be modernised in a world where technology and IT are transforming every aspect of life. This facilitates learning and supports independent learning. When students have access to Extramarks, they can learn at their convenience. Students can study for the exam at any time, whether late at night or early in the morning. They can achieve academic success without being confined to the retention of facts.
The use of Extramarks’ reference materials ensures that students are not merely retaining the material. The instructors of Extramarks have created the NCERT solutions to include a variety of questions, including theorybased, applicationbased and factual questions. Students can undertake indepth knowledge assessments with this help. Furthermore, Extramarks is popular among students who want to engage in elearning at a low cost.Everyone can receive a highquality education from Extramarks.
Additionally, Extramarks is committed to providing convenient and equitable access to students of all classes and education boards. Highquality education will have a broad range of effects in this way. Many of Extramarks’ features are well known for assisting students in passing their exams with flying colours. When students face challenges with regard to learning, they can ask the knowledgeable teachers of Extramarks for assistance. To answer all student questions, the teacher will hold an audio or video session. The documents with solutions provided by Extramarks can be downloaded more quickly because they are in PDF format. Students can get the chapter guide they require in a matter of seconds. Where there is a poor Internet connection, Extramarks extends its services. This will ensure that every student receives a highquality education.
Students do not need to inconvenience themselves to get assistance with regard to learning when they have Extramarks. One platform contains all the resources students will ever need to study effectively. Students can get assistance from a variety of teachers as well. Therefore, students can always speak with another teacher if they don’t understand how one teacher is explaining something. In order to spread education, Extramarks works to eliminate all obstacles.
Extramarks ensures that studying online has no disadvantages and offers solutions to turn those that do exist into benefits.
Additionally, images and textbooks can be shared between students and teachers. On the shared whiteboard, the instructor can post instructional materials before the start of the live session. Before starting the online session, the students can download and review the documents. Lectures cannot be replayed in a conventional classroom. Students can only try to take notes during the lecture quickly. Most educators forbid students from using their phones to record lectures inside the classroom. Accordingly, they may only attend the lecture once.
Model answers written by knowledgeable teachers are available in the questionandanswer guides. Combining these manuals, books, and live classes ensures that students do well on the test. Students gain the confidence required to ace the exam through a stepbystep, indepth revision. Extramarks has benefited many students, which is evidence that it has the potential to drastically alter the current elearning scenario. The nation’s future lies in education, and Extramarks is assisting the nation and its students in achieving success. There are numerous questions for students to practise answering in the NCERT textbook. Students can improve their grades in their Class 6 exams by practising with the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6, for instance. Students who are having trouble with Chapter 3 can use the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6. The Extramarks website and mobile application make it simple for students to access the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 and find their solutions.
Q.1 Find the HCF of the following numbers:
(a) 18, 48
(b) 30, 42
(c) 18, 60
(d) 27, 63
(e) 36, 84
(f) 34, 102
(g) 70, 105, 175
(h) 91, 112, 49
(i) 18, 54, 81
(j) 12, 45, 75
Ans.
$\left(\mathrm{a}\right)\text{}18,\text{}48\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}$
$\begin{array}{cc}2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}2& 48\\ 2& 24\\ 2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}18=2\times 3\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}48=2\times 2\times 2\times 2\times 3\\ \text{\hspace{0.17em}}\mathrm{HCF}=2\times 3=6\end{array}$
$\begin{array}{l}\left(\mathrm{b}\right)\text{}30,\text{}42\text{}\\ \text{}\begin{array}{cc}2& 30\\ 3& 15\\ 5& 5\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}2& 42\\ 3& 21\\ 7& 7\\ & 1\end{array}\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}30=2\times 3\times 5\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}42=2\times 3\times 7\\ \text{\hspace{0.17em}}\mathrm{HCF}=2\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}}=6\end{array}$
$\begin{array}{l}\left(\mathrm{c}\right)\text{}18,\text{}60\text{}\\ \text{}\begin{array}{cc}2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}2& 60\\ 2& 30\\ 3& 15\\ 5& 5\\ & 1\end{array}\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}18=2\times 3\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}60=2\times 2\times 3\times 5\\ \text{\hspace{0.17em}}\mathrm{HCF}=2\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=6\end{array}$
$\begin{array}{l}\left(\mathrm{d}\right)\text{}27,\text{}63\end{array}$
(e) 36, 84
(f) 34, 102
(g) 70, 105, 175
$\begin{array}{l}\begin{array}{cc}2& 70\\ 5& 35\\ 7& 7\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}3& 105\\ 5& 35\\ 7& 7\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}5& 175\\ 5& 35\\ 7& 7\\ & 1\end{array}\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}70=2\times 5\times 7\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}105=3\times 5\times 7\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}175=5\times 5\times 7\\ \text{\hspace{0.17em}}\mathrm{HCF}=5\times 7\text{\hspace{0.17em}}=35\end{array}$
(h) 91, 112, 49
$\begin{array}{l}\begin{array}{cc}7& 91\\ 13& 13\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}2& 112\\ 2& 56\\ 2& 28\\ 2& 14\\ 7& 7\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}7& 49\\ 7& 7\\ & 1\end{array}\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}91=7\times 13\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}112=2\times 2\times 2\times 2\times 7\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}49=7\times 7\\ \text{\hspace{0.17em}}\mathrm{HCF}=7\end{array}$
(i) 18, 54, 81
$\begin{array}{l}\begin{array}{cc}2& 18\\ 3& 9\\ 3& 3\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}2& 54\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.17em}}\begin{array}{cc}3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}18=2\times 3\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}54=2\times 3\times 3\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}81=3\times 3\times 3\times 3\\ \text{\hspace{0.17em}}\mathrm{HCF}=3\times 3=9\end{array}$
(j) 12, 45, 75
$\begin{array}{l}\begin{array}{cc}2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}}\begin{array}{cc}3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}\text{\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.17em}}\begin{array}{cc}3& 75\\ 5& 25\\ 5& 5\\ & 1\end{array}\end{array}$
$\begin{array}{l}\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}12=2\times 3\times 3\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}45=3\times 3\times 5\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}75=3\times 5\times 5\\ \text{\hspace{0.17em}}\mathrm{HCF}=3\end{array}$
Q.2 What is the HCF of two consecutive
(a) numbers?
(b) even numbers?
(c) odd numbers?
Ans.
(a) HCF of two consecutive numbers is 1.
(b) HCF of two consecutive even numbers is 2.
(c) HCF of two consecutive odd numbers is 1.
Q.3 HCF of coprime numbers 4 and 15 was found as follows by factorisation:
4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?
Ans.
No, it is not correct. HCF of 4 and 15 is not 0. HCF of 4 and 15 is 1.
FAQs (Frequently Asked Questions)
1. Can Extramarks answer all of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 questions?
The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 of “Playing with Numbers” contain a total of three questions. Extramarks will have the answers to all three questions for students. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 does not leave any questions unanswered. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 are explained in detail so that students understand how to form the correct answers. Students will easily understand the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 because remarkably talented teachers have prepared them to suit the intellect level of Class 6 students.
2. What concept should students study well in order to excel in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6?
The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 enclose three questions based on the concept of the Highest Common Factor or HCF. The highest (or greatest) of two or more given numbers’ common factors is the highest common factor (HCF). It is also known as the Greatest Common Denominator (GCD). HCF is a relatively easytounderstand but very significant concept. HCF will be used for many purposes in the future, so students must thoroughly understand the subject.
3. Is NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 easy?
Yes, NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 of “Playing with Numbers” encapsulate queries related to finding the Highest Common Factor of two numbers. HCF is a simple concept that students must practice. Students may refer to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 if they have questions about specific HCF concepts.
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8. What Important Formulas are included in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6?
In the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6, students will come across many crucial ideas. Every number is a factor, and knowing that different numbers and multiples play important roles in resolving equations will help them. Students must thoroughly read through all the questions and NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 to build a concrete conceptual foundation.
9. Do students need to practice all the questions in Playing with Numbers NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6?
Students should review every question in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.6 Playing with Numbers. They will gain confidence and a better understanding of the concepts as a result, which will make formula retention easier. It is highly recommended that students practice all of the questions about HCF and LCM because they are the two main highlights of this chapter. The problems cover different topics, enabling students to develop a stronger understanding of numbers.