# NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.5) Exercise 3.5

## NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.5) Exercise 3.5

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 consist of divisibility rules and prime factorization, which are two themes covered in Exercise 3.5 that are crucial for exam preparation. Based on the student’s level of comprehension, the divisibility rules are described in an approachable way. Prime factorization is the process of representing a number as the product of its factors.  Students will undoubtedly gain an understanding of the various methods that can be used to solve problems by practicing the NCERT Solutions for Class 6 Maths, Chapter 3, Exercise 3.5.

Extramarks’ NCERT Solutions for Class 6 Maths, Chapter 3, Exercise 3.5, can help students review prime factorisation and provide further explanation of divisibility rules.These NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5 cover the factor tree method as well as four divisibility rules.Class 6th Math Exercise 3.5, to which the NCERT Solutions to Class 6 Maths Chapter 3 Exercise 3.5 apply, is a lengthy exercise with a total of 12 questions.

The prime factorisation approach is used in Class 6 Maths Chapter 3 Exercise 3.5 to establish some fundamental principles of divisibility.In order to determine the prime factorisation of a number, students will also learn how to create factor tree diagrams. The links provided on the Extramarks website and mobile application will take students to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers.

### 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 3.6 3 Questions & Solutions Exercise 3.7 11 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 3 Playing with Numbers (Ex 3.5) Exercise 3.5

Through the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers students can learn the rules of divisibility with regard to other numbers by using the exercises of the chapter Playing with Numbers. Co-prime numbers are used as a foundation for several of the division rules in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers. Understanding these rules will assist students in dealing with each of the problems in these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers, which were compiled in collaboration with subject matter experts. The questions in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centered on Playing With Numbers come in a variety of styles, including word problems, factor trees, and extended answers. Another rule that is relevant in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centered on Playing With Numbers is that if a number is divisible by some other number, it is also divisible by each of that number’s factors.

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

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers and is  meant to be engaging and appealing, in keeping with the goal of making learning enjoyable. These NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5, centred on Playing With Numbers, will undoubtedly pique the interest of students because it describes a variety of games and activities.The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5, which focuses on Playing With Numbers, covers the following topics:

1. Multiples and factors
• A number’s exact divisor is referred to as a factor.
• In this section of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5, a game regarding the spotting element is provided. It is a must-try because it will entice students to understand various aspects of this topic in depth.
• The conclusion is that a number is a multiple of all of its constituent parts. NCERT Solutions For Class 6 Maths Chapter 3 Exercise 3.5 explain this in greater detail.
• Every number has a multiplier of one.
• Every number has a factor of one.
• A given integer has a finite number of factors.
• There are multiples of each number.
• A given integer has an unlimited number of multiples.
1. Numbers that are prime and composite
• Prime numbers are any numbers other than 1 with only the number itself and the number 1 as possible factors.
• Composite numbers are those that have more than two factors.
• The number one is neither a prime nor a composite.
• The smallest even prime number is 2.
• Every prime number except 2 is odd.
1. Evaluations for a number’s divisibility The following numbers’ divisibility tests are discussed:
• Ten-fold and five-fold divisibility
• 2 divided by 2
• 6 divided by 2
• 4 divided by 2
• 8-fold Divisibility
• 9-fold Divisibility
• 11-fold divisibility
1. Common multiples and factors
2. The use of prime factors
3. Highest Common Factor (HCF):

The highest common factor between any two or more given numbers is called the HCF.

1. Lowest common multiple:

The lowest common multiple (LCM) of two or more supplied numbers is called the common multiple.

1. A brief overview of HCF and LCM:

A lot of definitions, examples, exercises, graphics, flowcharts, and other extra reference materials are included in each part to make it more interesting. A summary is provided at the end of the chapter for rapid review.

### Chapter 3: Playing with Numbers (14 – 15)

The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers, are crucial and simple solutions by Extramarks. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centered on Playing With Numbers offer a step-by-step response to each of the chapter’s in-text problems. In these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on Playing With Numbers, students will study factors and multiples, prime and composite numbers, tests to determine whether a number is divisible, common factors and multiples, and so on. Students can develop the necessary conceptual foundation to comprehend complex topics by referring to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 for guidance. Extramarks professionals handpicked 500+ questions to cover every subject matter in addition to the NCERT Solutions for Class 6 Maths, Chapter 3, Exercise 3.5.A stable conceptual foundation and comprehension of understandable principles are essential for Maths as a subject. The format of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 is both educational and condensed. The idea is to make learning enjoyable for students while also assisting them in understanding the fundamentals.

Students can also access Extramarks’ study materials, such as explainers and 3D films, to gain a thorough understanding of the subjects, along with solutions to NCERT Class 6 Maths Chapter 3 Exercise 3.5. Students can fully immerse themselves in the extensive number of questions available in the practise section on Extramarks. The major points discussed in Chapter 3 to which the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 pertain are summarised below:

• Exercise 3.1 Introduction
• Exercise 3.2 Factors and Multiples
• Exercise 3.3 Prime and Composite Numbers
• Exercise 3.4 Tests for Divisibility of Numbers
• Exercise 3.5 Common Factors and Common Multiples
• Exercise 3.6 Some More Divisibility Rules
• Exercise 3.7 Prime Factorisation
• Exercise 3.8 Highest Common Factor
• Exercise 3.9 Lowest Common Multiple
• Exercise 3.10 Some Problems on HCF and LCM

Students can refer to the key ideas highlighted here while they study for their Maths exam:

• A number’s factor is the number that divides the quantity exactly.
• Every number has a factor of 1, and 1 is the only number with exactly one factor.
• A number is exactly divisible by a multiple of that number.
• A prime number is one that only has the number  itself and one other factor.In other words, the number itself and factor 1 are the only two different factors in a prime number.
• A composite number is a number that includes both the number itself and otherfactors other than 1.
• Twin primes are defined as primes that occur in pairs with a two-unit difference.

Extramarks offers NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 to help students better prepare for tests. Especially during independent study, it is vital to refer to solved cases and solution banks in order to comprehend the fundamental concepts and their applications. Many students find it challenging to understand Maths. Extramarks mentors have created a solution bank in the form of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5, which includes each stage in the problem-solving process, to help students understand exactly how they arrived at the required solution.

A number of numerical techniques are given in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 based on “Playing with Numbers” to help solve problems more quickly and easily. It is crucial to understand all these numerical shortcuts and guidelines so that students can apply them effectively to higher-level mathematical problems. These NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 serve as the subject’s foundation and include questions that are repeated in Class 8 with some trickier numerical techniques. These NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are significant because they serve as the foundation for a chapter that is addressed in Class 8.

Despite the fact that Maths is an application-based topic in every sense, these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 establish a very fundamental framework for mathematical inquiry. The solutions to Maths Class 6 Chapter 3 Exercise 3.5 cover a wide range of subjects, and each tip can be applied to the exercise that follows. The connection between factors and multiples, prime and composite numbers, tests for the divisibility of the integers 10, 5, 2, 3, 6, 4, 8, 9, and 11, prime factorisation, common factors and multiples, highest common factor, lowest common multiple, and other topics are covered in this NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5.

To help students understand how the method works when solving maths problems, the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 include the questions in the exercise and solved examples after discussing each of these aspects.Students in Class 6 should pay close attention to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5.Students can obtain the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 from the Extramarks website. They can download individual PDF files for NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 in this chapter from the website.

Before diving deeper into the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 students should first learn more about Arithmetic.

The study of numbers is a part of Maths called Arithmetic. Included in this are the characteristics of different numbers as well as the various operations, such as addition, subtraction, multiplication, and division. It is the most fundamental concept in the field of Maths and serves as the basis for all other concepts. Number theory is another name for Arithmetic. Man has long utilised this field of inquiry. The development can be seen of this topic starting in the prehistoric era and continuing through the first recorded uses of computations in the Egyptian and Roman Empires. Through a variety of theories and formulas used to assess numbers and results, the world as a whole has helped Arithmetic grow and develop.

mathematical operations other than the fundamental ones of addition, subtraction, multiplication, and division include square root, percentage, exponential, trigonometric functions, among many others. The various arithmetic expressions are assessed in accordance with the planned order of operations. The term “infix notation” refers to the most practical way to specify this. Students should also examine the subject’s fundamental procedures:

• Addition: Combining two or more integers to create a third number is known as addition.  Any number used in an operation is greater than the result.Addition is used to determine the outcome of a number combination.This most common mathematical operation is introduced to preschoolers shortly after the number system.
• Subtraction: The difference between the two integers is called subtraction. The response will be in positive integers if the number being subtracted from is greater than the starting number; otherwise, it will be in negative integers.
• Multiplication: Multiplication creates a third number, called the product, by adding two numbers together. The multiplier and multiplicand, or factors of the resultant number, are the two numbers. It is cumulative and associative to multiply. The square of any integer is the number times any other number. Any integer is equal to itself when it is multiplied by 1. Any number multiplied by 0 is 0; any positive integer multiplied by any other number produces a result that is more than the sum of the two factors.
• Division: Division is the exact opposite of Multiplication. A number is divided into equal parts. The number is divided into a number of parts, known as a quotient.  Dividend is the amount, and divisor is the amount used to calculate dividend.Any number is undefinable when divided by 0. Any number is equal to itself when it is split by one. Any number, when divided by itself, equals 1.

Aside from these four fundamental operations, Maths is subdivided into a number of disciplines and fields of study that are studied over the course of many years and are used everywhere. There are many different types of Maths, including decimal and compound unit Arithmetic. It is a fascinating area for investigation and study. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 cover a very little portion of the entire chapter. Nevertheless, the varied information and techniques are crucial.

Topics encased in these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are:

• Factors and multiples
• Prime and composite numbers
• Tests of divisibility of numbers
• Common factors and common multiples
• Some more divisibility rules
• Prime factorisation
• Highest common factor
• Lowest common multiple
• Some problems of HCF and LCM

### Factors and Multiples:

This section of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 is significant.When a number can be split completely without leaving any leftover by the first number, it is considered a factor of that number. A number is considered to have a factor if it can be divided exactly in two by another integer. A dividend is a factor of a divisor if the dividend is precisely divided by the divisor. The result of several specified numbers is a multiple. It is the outcome of multiplying two numbers together. In this subtopic of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5, students examine these two concepts as well as the different mathematical principles that they adhere to.

NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 contains a wealth of information on factors and multiples.The tasks that follow the examples with solutions might help students understand what is being said. Every number has a factor of 1. Additionally, it is clear that each number is a factor of itself and that each factor of a number is its exact divisor. This subtopic of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 also explains that every factor of a number is less than or equal to the number itself.

In addition, each multiple of a given number is greater than or equal to that same number. Consider the multiples of every conceivable integer. Students understand that there are an unlimited number of multiples of any number. Every number is a multiple of itself, students also realise. The concept of a “perfect number” is also covered in this subtopic. The definition of a perfect number is a number whose product of all factors is twice that number. Perfect numbers are 6 and 28. The activity that comes after this subtopic in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 has students apply the same guidelines and information that were previously provided. They can refer to the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 for assistance. These solutions are available on Extramarks. These problems have been resolved using a variety of techniques so that students can choose the one that works best for them. The real-world applications of these factors are many. Factors are quite helpful for a variety of things. The most fundamental application of factors is to divide something into equal pieces, to factor money in the banking industry, to compare costs, and to comprehend time.

### Prime and Composite Numbers:

Around 200 BC, Eratosthenes developed the concept of prime numbers. He developed an algorithm that determined the series’ prime numbers. Whole numbers are built on prime numbers. Prime numbers can be visually portrayed in a variety of ways.They are extremely important in the factorisation process.. A prime number is any whole number that can be divided exclusively by itself and by the number 1. We can state that there are only two elements in a prime number. A composite number is made up of many components. The integers 1 and 0 are neither prime nor composite numbers. Prime and composite numbers are used to categorise all whole numbers. Additionally, all whole integers are split into odd and even numbers. All multiples of 2, 3, 5, 7, and 11 are composite numbers. The multiples of 2 are referred to as even numbers. Odd numbers are the remaining numbers that are not multiples of two. The lowest prime even number is two. Every prime number—aside from 2—is an odd number. Indian Mathematician Srinivasa Ramanujan first used the phrase composite number in 1915.

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47 are all prime numbers up to a maximum of 50. The remainder is referred to as composite numbers up to 50. In order to handle more complex division and multiplication issues, it is required to make the distinction between prime and composite numbers. For better results, teachers recommend that students master  prime numbers at least up to 100. These NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 focus on how to apply and utilise these number divisions when dealing with mathematical problems. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 that follow this subtopic has solutions in Extramarks. These extremely helpful NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 have been put together by subject matter specialists at Extramarks. Prime numbers are applied in Asymmetric Cryptography, which has a practical application. In order to prevent reverberation and guarantee that the cogwheels wear equally, they are also utilised in Engineering in conjunction with co primes.

### Test of Divisibility of Numbers:

A rule to determine whether a number is divisible by another number is the test of divisibility of a number. Number divisibility has a long history that dates back to 500 CE. By this time, the Babylonian Talmud had recorded the divisibility test for the number 7. Since then, several techniques for dividing positive whole numbers have been developed, lost, and then rediscovered. The History of the Theory of Numbersby Leonard Dickson contains a summary of the divisibility tests. Some numbers have characteristics that allow students to quickly assess how divisible they are. Such tests of a few fundamental integers’ divisibility are covered in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5:

• Divisibility by 10 is determined by the presence of the digit 0 in the number’s unit position. For instance, the numbers 20, 3000, 40, and 60 may all be divided by 10, or in other words, they are all divisible by 10.
• If a number has 5 or 0 in its units place, it can be divided by 5 to determine its divisibility. Every number that can be divided by 10 can also be divided by 5.
• Any number that has the digits 2, 4, 6, 8, or 0 at its units position is divisible by 2. All even numbers can be seen to be divisible by 2. For instance, the numbers 632, 666, and 85552 are divisible by 2.
• Whether a number is divisible by three depends on whether the total of its digits is a multiple of three. For instance, the number 54. 5+4=9. 9 is a multiple of 3. Thus, 54 can be divided by 3.
• Any number that is divisible by both 2 and 3 is also divisible by 6. This means that the number must be an even number with a digit total that is a multiple of 3, as in 24, 60, 312, etc.
• Any number with three or more digits is divisible by four if the last two numbers are also divisible by four. 222324 is an illustration. Given that the last two digits of this number, 24, are divisible by four, the number itself is also divisible by four.
• When a number has more than four digits, it can only be divided by 8 if the final three digits, for example, 2104, may be divided by 8. Since the last three digits are 104, which can be divided by 8, the number 2104 can also be divided by 8.
• The divisibility test for the number 9 is the same as the test for the number 3. A number is nine digits divisible if the total of all of its digits is nine. For instance, 4608 has the following formula: 4+6+0+8=18. Since 18 is a multiple of 9, it can be concluded that 4608 is divisible by 9.
• If the difference between the sums of the digits in the odd positions from the right and the sums of the digits in the even positions from the right is a multiple of 11, divide the number by 11.
• All of these instruments are immediately used in the exercise that follows in these NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5.This is one of the most crucial aspects of Maths, and it appears frequently in the curriculum for upper-level classes. Students may check the Extramarks website to see how this and other divisibility tests are applied. Understanding the divisibility test makes it much easier to solve problems that are part of the Maths curriculum in senior classes.

Divisibility tests have practical applications in that they can be used to assess one object’s worth in relation to another; in other words, they can be applied to comparative studies. They are used to solve mathematical problems that arise in real-world situations quickly and effectively. They are widely applied in the banking industry to establish the allocation of costs. Engineers, particularly civil engineers and architects, also implement them.

### Common Factors and Common Multiples:

A number is said to be a common multiple of two or more numbers when it is a multiple of those numbers. The common factors of a number are two numbers that can be multiplied together to produce a third number. Numbers with just 1 in common between them are referred to as co-prime numbers. These are prime numbers, as the word would imply. The numbers 4 and 15 are co-prime. Extramarks’ NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 go into great length on this subject. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 should be referenced by students to gain a deeper understanding of the topic.

### Some More Rules of Divisibility:

The divisibility laws that were previously studied in this chapter are expanded upon in this subsection of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5. These guidelines aid in the speedy and effective resolution of mathematical problems. These are the rules that are listed in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5:

• Any number can be divided by any other number if that number itself can be divided by any other number. This implies that all of the number’s factors likewise function as multiples of the original number.
• Any number that can be divided by two co-prime numbers likewise can be divided by their product. According to this rule, the sum of any two co-prime numbers is also a multiple of the number that those two co-prime numbers are multiples of.
• If two given numbers can be divided by a certain amount, then their total can also be. In other words, the sum of two integers is divisible by a number of the added numbers, which are also divisible by each other.
• When two numbers are used and a number can be divided by both of them, the number can also be divided by their difference.

The solved exercise questions on the Extramarks website detail the procedures performed and the rationale behind the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5. They will aid students in better comprehending this subtopic in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5.

### Prime Factorisation:

A method for figuring out which prime integers, when multiplied, result in the given number is known as prime factorisation. In the case of integers, it was invented and originally utilised by Greek Mathematicians. They established that each positive integer could be divided into a number of prime factors, each of which could then be divided into integers. This is the basic tenet of Maths. Beginning with the smallest of all prime numbers that are 2, students should divide the provided number by that number. They should continue dividing until they reach a remainder or a decimal. The number should then be written as a composite of several prime numbers after being divided by 3, 5, 7, etc. Students can now learn Class 6 Maths by engaging in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 centred on the chapter named Playing with Numbers.

Prime factorisation’s practical use: The RSA encryption method has been well covered in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 focused on the chapter Playing with Numbers. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are compiled in a comprehensive and logically-sequenced manner to facilitate learning for students.

One of the most significant exercises in this chapter is the one that comes after this component. In addition to covering the final two rules of the lesson, the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 pertaining to the NCERT Maths textbook for Class 6 delve deeply into the rules previously presented in the chapter. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 begin with a true or false question before moving on to factorisation strategies. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 provide examples for each rule of the divisibility tests and factorisation in general. This and many other answers to the tasks in these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are available on the Extramarks website. These NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are really helpful, especially for last-minute homework and studying. If students decide to pursue higher education in the field of Engineering, whether it be civil, mechanical, or ENTC, prime factorisation will be used later on. Students should visit the Extramarks website for additional information on these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 as it addresses  in great detail.

### Highest Common Factor:

The highest number that can be divided exactly into two or more other numbers is the highest common factor, sometimes referred to as the greatest common divisor. This is used to make a factor simpler. Finding the factors of both numbers, identifying the common factors, and then identifying the highest common factor can help students identify the highest common factor. In order to identify the number that may be or is very close to the highest common factor, they can also determine all the common prime factors. Alternately, one can fiddle with the integers until they find their highest common factor. One of the bestknown concepts and guidelines taught in these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 is this. These methods have been discussed in extensive detail in the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5.

The Euclidean algorithm is the process used to determine the highest common factor. Even after some small adjustments, computer programming still makes use of this incredibly effective method. It is applied to divide a common element into its simplest forms. They can use it to locate the integer solutions to linear equations, which is another very helpful function. Students can use the tools and examples encapsulated in Extramarks’ NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 to successfully complete their assignments and get high test scores.

Additionally, these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 must be completed successfully because they serve as the basis for several topics in higher Classes. The Extramarks website includes separate solutions for each of the exercises in this chapter. The NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 should therefore be referred to more  often for good practise.

### Lowest Common Multiple:

The lowest number that can be divided into two or more different numbers is referred to as the lowest common multiple. It is sometimes referred to as the LCM which stands for lowest common multiple. Finding the prime factors of each number and identifying the shared prime factors is one of the most popular methods for determining the lowest common multiple of a number. Find the number’s biggest common factors and then divide these afterwards. Multiply the result by further numbers. To learn more about the techniques used to find the Lowest Common Multiple of supplied integers, students should refer to the Extramarks. In contrast to other subjects, studying Maths diligently is much more likely to yield a perfect score. Students can accomplish this by understanding the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 with the aid of Extramarks and their experts.

### Some Problems of HCF and LCM:

The next section of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 gives some examples of how to find the highest common factor and lowest common multiple of two values. Through these NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5, students can see how several approaches can be used to identify the required lowest common multiple or highest common factor.The HCF and LCM can be determined by a variety of methods. By division method and by prime factorization method are two of the most used in the NCERT Solutions for Class 6 Maths, Chapter 3 Exercise 3.5.

### HCF and LCM Tricks and Formulae:

• The sum of two numbers’ Highest Common Factor and Least Common Multiple is known as their product.
• Highest Common Factor is calculated by dividing the Least Common Multiple of the numerator by the Highest Common Factor of the enumeration.
• The Least Common Multiple is calculated by dividing the Highest Common Factor of the Denominator by the Least Common Multiple of the Numerator.

In addition to these solutions of Exercise 3.5 enclosed in NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5, the Extramarks website provides a tonne more solved examples for LCM and HCF. Students can use these to comprehend the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 in a sophisticated manner. Due to its rigorous technique, this idea is covered in great length on the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 and has proven to be especially helpful to refer to in the future. The ability to score well in Maths can influence a student’s average percentage and grade.

Class 6 Maths Chapter 3 is titled “Playing With Numbers” of which the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are a major part. The ideas of “Some More Divisibility Rules” and “Prime Factorisation” are the foundation of NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5. Students will learn additional divisibility rules in these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5, which they will apply when answering questions. Additionally, they will learn how to divide the provided numbers into their prime factors with the aid and assistance of the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5. prime factorisation is implemented in the RSA encryption process, which is how it is applied in real life. Understanding the themes in the chapter in a better way will be made possible with the help of this NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5.

On the Extramarks website, students may obtain the NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 based on Playing with Numbers. The steps for obtaining these NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.5 are listed below:

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Q.1 Which of the following statements are true?
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) A number is divisible by 18, if it is divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Ans.

(a) False,
(b) True,
(c) False,
(d) True,
(e) False,
(f) False,
(g) True,
(h) True,
(i) False.

Q.2 Here are two different factor trees for 60. Write the missing numbers.
(a)

(b)

Ans.

Factor trees with missing numbers are given below:

(a)

(b)

Q.3 Which factors are not included in the prime factorisation of a composite number?

Ans.

1 and number itself are not included in the prime factorization of a composite number.

Q.4 Write the greatest 4-digit number and express it in terms of its prime factors.

Ans.

$\begin{array}{l}\text{The greatest 4}-\text{digit number}=\text{9999}\\ \text{}\text{}\text{}\text{}3\overline{)9999}\\ \text{}\text{}\text{}\text{}3\overline{)3333}\\ \text{}\text{}\text{}\text{}11\overline{)1111}\\ \text{}\text{}\text{}\text{}\text{}\text{}101\overline{)101}\\ \text{\hspace{0.17em}}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{}\overline{)1}\\ \text{Prime factor of 9999}=\text{3}×\text{3}×\text{11}×\text{1}0\text{1}\end{array}$

Q.5 Write the smallest 5-digit number and express it in the form of its prime factors.

Ans.

$\begin{array}{l}\text{The smallest 5}-\text{digit number}=\text{1}0000\\ \text{}\text{}\text{}\text{}2\overline{)10000}\\ \text{}\text{}\text{}\text{}2\overline{)5000}\\ \text{}\text{}\text{}\text{}2\overline{)2500}\\ \text{}\text{}\text{}\text{}2\overline{)1250}\\ \text{}\text{}\text{}\text{}5\overline{)625}\\ \text{}\text{}\text{}\text{}5\overline{)125}\\ \text{}\text{}\text{}\text{}5\overline{)25}\\ \text{}\text{}\text{}\text{}5\overline{)5}\\ \text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\overline{)1}\\ \text{Prime factors of 1}0000\text{}=\text{2}×\text{2}×\text{2}×\text{2}×\text{5}×\text{5}×\text{5}×\text{5}\end{array}$

Q.6 Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.

Ans.

$\begin{array}{l}7\overline{)1729}\\ 13\overline{)247}\\ \text{\hspace{0.17em}}19\overline{)19}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\overline{)1}\\ \text{Prime factors of 1729}=7×13×19\\ \mathrm{The}\text{difference between two consecutive prime factors is 6.}\end{array}$

Q.7 The product of three consecutive numbers is always divisible by 6. Verify this statement with the help of some examples.

Ans.

Let us take three consecutive numbers as 2, 3, 4.

Product of three numbers = 2 × 3 × 4

= 24, which is divisible by 6.

Let us take another three numbers as 11, 12, 13.

Product of these three numbers = 11 × 12 × 13

= 1716, which is divisible by 6

In this way, we see that product of three consecutive numbers is always divisible by 6.

Q.8 The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.

Ans.

Let us take two consecutive odd numbers as 3 and 5. Then, their sum = 3 + 5
= 8, which is divisible by 4.

Let us take another set of two consecutive odd numbers as 17 and 19.Then,

Sum of numbers = 17 + 19

= 36, which is divisible by 4.

Thus, the sum of two consecutive odd numbers is divisible by 4.

Q.9 In which of the following expressions, prime factorisation has been done?
(a) 24 = 2 × 3 × 4 (b) 56 = 7 × 2 × 2 × 2
(c) 70 = 2 × 5 × 7 (d) 54 = 2 × 3 × 9

Ans.

In option (b) and (c), prime factorisation has been done because 2, 5 and 7 are prime numbers. While 4 and 9 are not prime numbers which are given in option (a) and (d).

Q.10 Determine if 25110 is divisible by 45.

Ans.

A number will be divisible by 45 if it is divisible by 5 and 9.
Given number 25110 is divisible by 5 because one’s digit is 0.
Now, 2 + 5 + 1 + 1 + 0 = 9 is divisible by 9. So, 25110 is also divisible by 9.
Therefore, we can say that 25110 is divisible by 5 and 9 together, so it is divisible by 45.

Q.11 18 is divisible by both 2 and 3. It is also divisible by 2 × 3 = 6. Similarly, a number is divisible by both 4 and 6. Can we say that the number must also be divisible by 4 × 6 = 24? If not, give an example to justify your answer.

Ans.

A number which is divisible by 4 and 6 is not divisible by 24. There is a example to prove it. 12 is divisible by 4 and 6 but it is not divisible by 24.

Q.12 I am the smallest number, having four different prime factors. Can you find me?

Ans.

Four smallest prime numbers are 2, 3, 5 and 7.

So, the smallest number = 2×3×5×7
= 210