NCERT Solutions for Class 6 Maths, Chapter 3 - Playing With Numbers

This chapter introduces the concept of divisors and factors. The divisor is any number that divides another number. A factor,  however, is a divisor that divides the number entirely and leaves no remainder. So, all factors of a number are its divisors. But not all divisors will be factors.

In NCERT Maths Book Class 6, Chapter 3 Solutions, as you progress through the chapter factors and divisors add fun to the chapter in the form of a game that the students can play!  They will learn about prime and composite numbers, a very important and fundamental topic of mathematics introduced in playing with numbers class 6 questions. As the chapter progresses students will learn about prime factorization, some more divisibility rules, highest common factor, lowest common multiple. At the end of this chapter, you will be able to develop a grip and understand prime and composite numbers in depth.

Let’s take a look at topics and sub-topics of Class 6 Maths Chapter 3, Playing With Numbers

3.1 Introduction

3.2 Factors and Multiples

3.3 Prime and Composite numbers

3.4 Tests for Divisibility of Numbers

3.5 Common factors and common multiples

3.6 Some more divisibility rules

3.7 Prime Factorization

3.8 Highest Common Factor

3.9 Lowest Common Multiple

3.10 Some Problems on HCF and LCM

In Class 6 Maths NCERT Solutions Chapter 1, you will learn – 

Section 3.2 – In this section, you’ll study about factors and multiples. As you move further some facts related to factors and multiples are introduced like a ‘1 is a factor of every number’, ‘Every number is a factor of itself, ‘Every factor of a number is an exact divisor of that number ’, ‘Number of factors of a given number is finite’, ‘Every multiple of a number is greater than or equal to that number’, ‘Every number is a multiple of itself’ etc.

Section 3.3 – This section will brief you about prime and composite numbers. Prime numbers are those whose only factors are 1 and the number itself. The smallest prime number is 2. Composite numbers are those whose factors are greater than 2. The smallest composite number is 4. As you move further you’ll study the algorithm known as ‘Sieve of Eratosthenes’ given by Greek mathematician Eratosthenes. This algorithm helps to find out all the possible prime numbers in a range.

Section 3.4 – In this section, you’ll study the tests required for the divisibility of numbers. This section comprises of several facts and tests that are necessary to check the divisibility of a number. If you want to check whether a number is divisible by 2 or not then it is not required to divide the number just check the last digit of that number if that digit is even then the number is divisible by 2. In case of the divisibility by 5 if the last digit is 0 or 5 then only the number is divisible by 5. As you move further in this section you will learn some more interesting facts related to divisibility.

Section 3.5 – You already know what are factors and multiples. Now you’ll study about common factors and common multiples. In section 1.2 you have studied the factors and multiples of a number but if two numbers are considered then we have to take the factors and multiples which are common to both. As you move further in this section you will learn what co primes are and how to write down the common factors and multiples.

Section 3.6 – In this section, some more divisibility rules are introduced. In section 1.4 some tests and rules related to divisibility were introduced now you’ll study the divisibility rules for some large numbers and some facts related to divisibility rules. For example, ‘If a number is divisible by two co-prime numbers then it is divisible by their product also ’. This section requires the knowledge that you have gained from section 1.4

Section 3.7 – Earlier in this chapter you have studied what factorization is. This section helps you in understanding the concept of prime factorization. When a number is expressed as the product of its prime factors we say that the number is factorized with its primes. The prime factorization of a number is always unique. It uses the concept of factor tree to break down a number into its prime factors.

Section 3.8 – You already know what are common factors. This section will teach you how to find out the highest common factor (HCF) multiple numbers. It is also known as the greatest common divisor or GCD. The HCF of two or more numbers is the highest (or greatest) of their common factors. It can be found out by writing all the common factors or by only writing the prime factors.

Section 3.9 – You already know what are common multiples. This section will teach you how to find out the lowest common multiple (LCM) multiple numbers. The lowest common multiple or LCM of two or more given numbers is the lowest (or smallest or least) of their common multiples. This section also uses the concept of prime factorization.

Section 3.10 –This section comprises of many problems related to the highest common factor (HCF) and lowest common multiple (LCM). You can practice several problems of different difficulty level.

In this chapter, you are provided with several examples along with their solutions for a clear understanding of numbers. To know more about NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers., you should explore the exercises below. You can also download the Knowing our Numbers Class 6 NCERT Solutions PDF, solved by expert mathematics trainers. You can also refer online to Class 6 Maths Chapter 3 Worksheet PDF.