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CBSE Class 6 Mathematics Chapter 3 Revision Notes – Playing With Numbers
Extramarks’ Class 6 Mathematics Chapter 3 Notes are curated by subject matter experts in pointers to help students grasp the chapter’s concepts easily. These notes provide all of the major points in the chapter in a wellstructured manner. With these notes, students can develop conceptual clarity and a better understanding of the topics.
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Revision Notes For CBSE Class 6 Mathematics Chapter 3
CBSE Class 6 Mathematics Chapter 3 Notes will help students revise the core concepts in the shortest time. All the concepts have been illustrated with suitable examples so that students can understand them easily. These notes are available on the website. Students can access these notes at their convenience.
Introduction To CBSE Class 6 Mathematics Chapter 3 Revision Notes
The revision notes on Chapter 3 “Playing With Numbers” of Class 6 Mathematics deal with the basic concepts of factors, multiples, prime numbers, composite numbers, and the rules of divisibility along with HCF and LCM. All the terms associated with this chapter are explained in an easy way. Students will be able to solve problems with confidence once they go through these notes properly.
Class 6 Mathematics Chapter 3 Revision Notes
A number is an arithmetical value that can be expressed using words, symbols, and numbers. These numbers can be expressed in the generalised form as singledigit, doubledigit, or threedigit numbers.
The topics covered in Class 6 Mathematics Chapter 3 Notes include:
Types of Numbers: A system for writing numerical expressions is referred to as a number system. There are various types of numbers in the number system, which are:
 Composite numbers
 Natural numbers
 Odd numbers
 Prime numbers
 Seven numbers
 Whole numbers
Factor: If a number divides another number exactly, then the divisor is called a factor of that number. For example, if 10 is divided by 2 or 5 it leaves no remainder. Therefore, 2 and 5 are factors of 10.
Properties of a Factor
 Every number is exactly divisible by its factor.
 1 is a factor of every number as it divides every number evenly.
 Every number is a factor of itself as every number is exactly divisible by itself.
 Factors must be less than or equal to the given number.
 Every number has a fixed number of factors.
Multiple: If a number is multiplied by an integer, the product is called the multiple of that number. For example, the multiples of 2 are 4, 6, 8, 10, 12 etc.
Properties of a Multiple
 Every number is a multiple of itself.
 Multiples can never be smaller than the number itself.
 The number of multiples of a given number is infinite.
Difference between Factor and Multiple
 A factor is an exact divisor of a given number, whereas, a multiple is the product of a given number and an integer.
 Factors can be less than or equal to the given number. However, multiples are greater than or equal to the given number.
 The number of factors of a given number is limited, but the number of multiples of a given number is infinite.
Common Factor and Common Multiple: A factor which is common in two or more numbers is called a common factor. Similarly, a multiple which is common in two or more numbers is called a common multiple.
 Consider two numbers, 8 and 10. The factors of 8 are 1, 2, 4, and 8. Factors 10 are 1, 2, 5, and 10. Therefore, 2 is a common factor of both numbers.
 The multiples of 5 are 10, 15, 20, 25, 30, 35, 40 etc. The multiples of 7 are 14, 21, 28, 35, 42, 49, etc. The multiple 35 is common in both cases. Hence, 35 is a common multiple of 5 and 7.
 If two or more two numbers have only one common factor and that is 1, then the numbers are called coprime numbers. For example, 2, 5, and 41 are coprime numbers.
Prime Numbers: Prime numbers are those numbers which are divisible by 1 and that number only. For example, 2, 3, 5, 7, 11 etc. are prime numbers.
 1 is not a prime number.
 2 is the smallest prime number.
 2 is the smallest even prime number.
 3 is the smallest odd prime number.
 All prime numbers are odd numbers except 2.
Composite Numbers: Composite numbers are those which are divisible by more than two factors. For example, consider the number 6. It is divisible by 1, 2, 3, and itself. So, it has four factors. Therefore, it is a composite number.
 1 is not a composite number since it has one factor only, that is, 1.
 Therefore, 1 is neither a prime number nor a composite number.
Perfect Numbers: A perfect number is one where the total of all its factors is twice the number.
For example, 1, 2, 4, 7, 14, 28, and 56 are the factors of 56.
Here, 1 + 2 + 4 + 7 + 14 + 28 = 56, which also equals to 2 x 28
As a result, the total of 28 factors equals double the number of 28.
Rules Of Divisibility
Divisibility by 10
 A number is divisible by 10 if it has zero at its ones place.
 For example, 20, 30, 40, 100, 300, and 1000 all are divisible by 10.
Divisibility by 5
 A number is divisible by 5 if it has zero or five at its ones place.
 For example, 10, 15, 20, 25, 55, 75, 95, etc., are divisible by 5.
Divisibility by 2
 A number is divisible by 2 if it has an even number at ones place.
 In other words, the numbers which have 2, 4, 6, or 8 in their ones place are divisible by 2.
 For example, 12, 24, 36, 88, etc., are divisible by 2.
Divisibility by 3
 A number is divisible by 3 if the sum of its digits is exactly divisible by 3.
 For example, suppose 102 is a given number. The sum of its digits 1, 0 and 2 is divisible by 3, ie., 1 + 0 + 2 = 3, which is divisible by 3. Therefore, the number 102 is divisible by 3.
Divisibility by 4
 A number with three or more digits is divisible by 4 if the number formed by its last two digits is divisible by 4.
 For example, 412, 1020, 5028 etc. are divisible by 4 because the numbers formed by the digits of tens place and ones place are divisible by 4.
 Therefore, a number with three or more digits is divisible by 4 if the number formed by its last two digits is a multiple of 4.
 In the case of singledigit or doubledigit numbers, divisibility has to be checked by actual division.
Divisibility by 6
 A number is divisible by 6 if it is divisible by both 2 and 3.
 For example, the number 36 is divisible by both 2 and 3. So, it is also divisible by 6.
Divisibility by 8
 A number with three or more digits is divisible by 8 if the number formed by the last three digits is divisible by 8.
 For example, 2000, 2416, 3104, etc. are divisible by 8.
 Divisibility for two or threedigit numbers must be checked by actual division.
Divisibility by 9
 A number is divisible by 9 if the sum of its digits is divisible by 9.
 For example, consider the number 198. The sum of its digits 18 is divisible by 9.
 Therefore, the number 198 is divisible by 9.
Divisibility by 11
 A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is zero or exactly divisible by 11 itself.
 For example, consider a number, say 592845.
 The sum of the digits at odd places = 9 + 8 + 5 = 22.
 The sum of the digits at even places = 5 + 2 + 4 = 11.
 The difference between the sums = 22 – 11 = 11.
 11 is divisible by itself.
 Therefore, the number 592845 is also divisible by 11.
Some More Rules of Divisibility
 When a given number is divisible by another number, then the given number must be divisible by all the factors of the divisor.
 For example, 24 is divisible by 12.
 The factors of 12 are 1, 2, 3, 4, 6, and 12.
 Then 24 is also divisible by 2, 3, 4, and 6.
 If any two numbers are divisible by a certain number, then the sum of the two numbers is also divisible by the certain divisor.
 For example, 10 and 25 are divisible by 5.
 Therefore, the sum of 10 and 25, that is, 35 is also divisible by 5.
 If two coprime numbers divide a given number exactly, then their product also divides the given number exactly.
 For example, 105 is divisible by the coprime numbers 5 and 7.
 Then 105 is also divisible by the product of 5 and 7, that is, 35.
 If two numbers are divisible by a certain divisor, then their difference is also divisible by that divisor.
 For example, 20 and 30 are divisible by 5.
 Then the difference between 30 and 20, 10, is also divisible by 5.
Prime Factorisation: The method of expressing a number as a product of its prime factors is called prime factorisation.
 For example, 24 can be written as 2 × 2 × 2 × 3. 2 and 3 are the prime factors.
Highest Common factor (HCF) and Least Common factor (LCM)
 The HCF is the highest or greatest factor common in two or more numbers.
 The LCM is the smallest multiple commons in two or more numbers.
 For example, 10 and 15 are the given numbers.
 Prime factorisation of 10 = 1 × 2 × 5.
 Prime factorisation of 15 = 1 × 3 × 5.
 Therefore, the HCF = 1 × 5 = 5.
 And, the LCM = 1 × 2 × 3 × 5 = 30.
Why Refer to Extramarks for CBSE Class 6 Mathematics Revision Notes?
With the right study materials and practice, students can score better marks in Mathematics. Extramarks is an ideal study partner as students can easily access concise and precise Class 6 Mathematics Revision Notes from the website. They can refer to these notes and gain conceptual clarity in every topic and answer every question with confidence.
The notes are prepared meticulously by subject matter experts to help students perform better in exams. Every topic is illustrated with examples so that they can understand the logic behind the statements. All of the major points given in the revised CBSE syllabus for Mathematics are covered in detail.
Expert Tips on CBSE Class 6 Exam Preparation
Here are some tips for students to improve their Class 6 exam preparations:
 Time Management
Making a schedule for studies helps students utilise the maximum time before the exam. They can revise the points that they have read and practised before answering the questions. However, they should also take some time to relax. During these study breaks, students can meditate, create art, or listen to music.
Time management is also crucial in the exam hall. Students must first read the questions and then attempt the questions they are most confident in. It is important to not get stuck on a question. Leave it for later inspection and move on to the next question. An additional tip is to practise writing neatly at a fast pace to make answers presentable.
 Write the Points
Practice makes one perfect. Therefore, students may write the points in their own understanding so that it is easier to remember them. It will also help them understand how much time should be given to each question or topic in the exam.
 Make Your Own Diagrams
Visual representation is always helpful in understanding a topic. Drawing small diagrams will help students grasp all of the ideas in one go. Mind maps can be used to understand the connections between two concepts. So, students can make their own diagrams and glance at them before entering the exam hall.
 Write with Confidence
Many students often score poor marks in exams despite having strong preparation. The main reason for it is a lack of confidence. Students often become stressed and start making mistakes. The key here is to write with confidence. With good time management, students can take the last 1015 minutes to review their answers and check if the correct question numbers are written beside the answers before submitting the answer script.
FAQs (Frequently Asked Questions)
1. Write the first three multiples of 12.
The first three multiples of 12 are 12, 24, and 36.
2. Are 5 and 11 coprime numbers?
The prime factorisation of 5 and 11 are 1 × 5 and 1 × 11 respectively. 1 is their only common factor. Therefore, 5 and 7 are coprime numbers.
3. Find the common factors of the coprime numbers 29 and 47.
All the coprime numbers have only one common factor, that is, 1. So, the answer will be 1.