Playing With Numbers Class 6 Notes CBSE Maths Chapter 3 (Free PDF Download)

Factors And Multiples

Factors:

• If a number $n$ is the exact divisor of the number $m$ then $n$ is the factor of $m$ i.eThe factor of a number is the exact divisor of that number.

• A number always has at least two factors i.e., $1$ and the number itself.

• Every factor is less than or equal to the given number and is finite.

• For example: Factors of $20$ are $2,10,5$ and $4$ 

• A perfect number is whose sum of all the factors is equal to twice the number.

Multiples:

• Multiple is the product of two or more numbers

• A number always have at least one multiple i.e., the number itself

• Multiples is always greater than or equal to the given number and multiples of a number is infinite.

• For example: $5\times 4=20$ here $20$ is the multiple of $5$ and $4$

Prime And Composite Numbers

• Prime numbers are the numbers which are divisible only by $1$ and the number itself i.e., a prime number always have only two factors.

• $2$ is the only prime number which is even and all other prime numbers are odd.

• For example: $2,3,5,7,11,13,17$ etc. are the prime numbers

• Composite numbers are the numbers which are divisible by more than two factors i.e., composite number have more than two factors.

• For example: $4,6,8,10,12,14,$ etc.

• $1$ has only one factor i.e., $1$ itself so it is neither prime nor composite number.

• Even numbers are those number which are the multiples of $2$ 

• Odd numbers are those number which are not the multiples of $2$

Test for Divisibility of Numbers

1. Divisibility by $10$ 

• A number is divisible by $10$ when its ones digit is $0$ then only it is the multiple of $10$ 

• For example: $520,950,630,20$ etc.

2. Divisibility by $5$

• A number is divisible by $5$ when its ones digit is either $0$ or $5$ then only it is the multiple of $5$ 

• For example: $50,95,65,20$ etc.

3. Divisibility by $2$ 

• A number is divisible by $2$ when its one’s digit is $0,2,4,6$ or $8$ i.e., every even number is divisible by $2$ 

• For example: $50,92,64,26,68$ etc.

4. Divisibility by $3$ 

• A number is divisible by $3$ when sum of its digit is divisible by $3$ 

• For example: $7263$, the sum of digits of $7263$ is $18$ and $18$ is divisible by $3$ therefore $7263$ is also divisible by $3$

5. Divisibility by $6$ 

• A number is divisible by $6$ only if it is divisible by $2$ and $3$ both.

• For example: $6,12,18,24,36$ etc.

6. Divisibility by $4$ 

• One digit and two-digit number divisibility by $4$ is checked by actual division.

• But three or more-digit number is divisible by $4$ if the number formed by the last two digit is divisible by $4$ 

• For example: $1000,3012,523612$ etc.

7. Divisibility by $8$ 

• One digit to three-digit number divisibility by $8$ is checked by actual division.

• But four or more-digit number is divisible by $8$ if the number formed by the last three digit is divisible by $8$ 

For example: $1000,3012,523612$ etc.

8. Divisibility by $9$

• A number is divisible by $9$ when sum of its digit is divisible by $9$ 

• For example: $215847$,  the sum of digits of $215847$ is $27$ and $27$ is divisible by $9$ therefore $215847$ is also divisible by $9$

9. Divisibility by $11$ 

• If the difference between the sum of the digits at odd places and the sum of the digits at even places of the number is either $0$ or divisible by $11$, then the number is divisible by $11$ 

• For example:

$61809$ 

• Sum of digits at odd places$=6+8+9=23$ 

• Sum of digits at even places$=1+0=1$ 

• Now, difference between the sum of the digits at odd places and the sum of the digits at even places$=23-1=22$ 

• Since, $22$ is divisible by $11$ 

• Therefore, $61809$ is also divisible by $11$

Common Factor Or Common Multiple

• A factor which is common in two or more numbers is called common factor.

• For example: 

• Factors of $8$ are $1,2,4$ and $8$ 

• Factors of $12$ are $1,2,3,4,6$and $12$ 

• $\therefore 4$ is the common factor of $8$ and $12$ 

• A multiple which is common to two or more numbers is called common multiple.

• For example: 

• Multiple of $2$ are $4,6,8,10,12$ and $18$ 

• Multiple of $3$ are $6,9,12,15,18$ and $21$ 

• $\therefore 6,12$ and $18$ are common multiple of $2$ and $3$ 

• Co-prime are those number which have $1$ as common factors.

• For example: $5,8,69,52,41$ etc. are co-primes

Some More Divisibility Rules

1. If a number is divisible by another number, then it is divisible by each of the factors of that number.

For example: $12$ is divisible by $6$

• Factors of $6$ are $1,2,3$and $6$ 

• Therefore, $12$ is also divisible by $1,2$ and $3$ 

2. If a number is divisible by two co-prime numbers, then it is divisible by their product also.

For example: 

• $160$ is divisible by $8$ and $5$ which are co-primes 

• Product of $8$ and $5$ is $40$ 

• Therefore, $160$ is also divisible by $40$ 

3. If two given numbers are divisible by a number, then their sum is also divisible by that number.

For example: 

• $15$ and $10$ are divisible by $5$ 

• Sum of $15$ and $10$ is $25$ which is also divisible by $5$ 

4. If two given numbers are divisible by a number, then their difference is also divisible by that number

For example: 

• $15$ and $10$ are divisible by $5$ 

• Difference of $15$ and $10$ is $5$ which is also divisible by $5$

Prime Factorization

• The method of representing number as a product of its factors is called prime factorization.

• For example: $36$ can be written as $2\times 2\times 3\times 3$, $2$ and $3$ are prime numbers.

Highest Common Factor

• HCF of two or more number is the highest or greatest factor among all the common factors.

• For example:

• Factors of $60$ are $2\times 2\times 3\times 5$ 

• Factors of $28$ are $2\times 2\times 3\times 7$ 

• Common factors are: $2$ and $3$ 

• Highest common factor is $3$

Lowest Common Multiple

• LCM of two or more number is the lowest multiple among all the common multiples

• Simply, product of the prime factors of two or more number is called LCM counted the maximum number of times they occur in any of the numbers.

• For example: 

• Prime factorization of $30$ is $2\times 3\times 5$ 

• Prime factorization of $4$ is $2\times 2$

• LCM of $15$ and $4$ is $2\times 2\times 3\times 5=60$

Revision Notes for CBSE Class 6 Maths Chapter 3 - Free PDF Download

The chapter has seven exercises that include types of numbers, factors and their properties, multiples, prime and composite numbers, divisibility test of numbers, common multiples, common factors, prime factorisation, highest common factor, lowest common multiple and some practising problems based on LCM and HCF.

There are revision questions for practice related to all the topics mentioned above. These problems have been divided into 7 exercises from 3.1 to 3.7 for the students to identify the topics easily.

Introduction To CBSE Class 6 Maths Revision Notes

Introduction to CBSE Class 6 Maths Before you download the PDF, read some of those points that we have stated below. These are very basic revision notes and once you download the PDF, you will have more significant insights into the subject and there are high chances that you will perform better.

Playing With Numbers Class 6 Notes Revision notes that Vedantu provides will help you in understanding the core parts of that particular chapter and let you prepare well for the exam that you’ll be appearing in.

Class 6 Maths Chapter 3 Revision Notes

Our practise papers usually allow you to understand the pattern and the weightage of the subject and help you practice the same. In addition, we also add the important questions from the previous years so that you can master the subject before you appear for the examination.

A number is defined as an arithmetical value, expressed by words,  symbols, and figures. These numbers can be written either in single-digit format, double digits format, the three-digits format in the generalized form.

1. Types of Numbers

A number system is a system of writing the expression of numbers. According to the number system, there are different types of numbers. They are:

• Prime numbers

• Seven numbers

• Odd numbers

• Whole numbers

• Natural numbers

• Composite numbers

2. Factors

A factor of a number is a divisor of the number itself.

Example: 3, 4, 6, 9, 12, and 36 are the factors of 36.

3. Properties of Factors

• 1 is a factor of every number.

• Every number is a factor of itself.

• Every factor of a number is an exact division of that number.

• Every factor of a given number is greater than or equal to the number.

4. Perfect Numbers

A perfect number is one of the types of numbers that has the sum of all the factors equal to twice the number.

Example: Factors of 56: 1, 2, 4, 7, 14, 28, and 56

Here, 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 x 8

Therefore, the sum of factors of 28 is equal to twice the number of 28.

5. Multiples

Multiples of a number are those numbers that we get on multiplying the number by an integer.

Examples: Multiples of 3 are 6,9,12,15,18 etc.

6. Properties of Multiples

• There are infinite multiples of a given number.

• Every number is a multiple of itself.

7. Prime Numbers

The numbers whose factors are 1 and the number itself are called Prime numbers.

Example: 2, 3, 5, 7 etc.

8. Composite Numbers

Numbers having multiple factors are called Composite numbers.

Example: 4, 6, 8 etc.

Divisible by 2 or 5 or both 2 and 5.

9. Divisibility Tests

• Divisibility Test for 2

• Divisibility Test for 4

• Divisibility Test for 3

• Divisibility Test for 5

• Divisibility Test for 8

• Divisibility Test for 6

• Divisibility Test for 7

• Divisibility Test for 9

• Divisibility Test for 10

• Divisibility Test for 11

10. Common Factor

1. Common Multiples

Why Refer To Vedantu For CBSE Class 6 Maths Revision Notes PDF?

We provide materials on NCERT Solutions for Class 6 Chapter 3 Playing with numbers in an accessible format.

Apart from this, we also provide notes, question papers and other learning materials in PDF format, which you can download and access offline as well. Also, by solving sample papers and previous year question papers through our website, you will get an idea of the exam pattern for Chapter 3 that will work as a helping hand for you in standing ahead in the exam preparation.

Expert Tips on CBSE Class 6 Exam Preparation

1. Have a positive attitude towards the exam

2. Set a deadline for each topic. This will help to finish all the subjects within the time.

3. After you have completed studying, you must revise all that you have already studied. 

4. Set your studying schedule and pick a peaceful place to study.

5. Set some time to refresh your memory. So, do some engaging activities regularly.

6. Ensure that you have enough sleep time

7. Before the exam, do not read any new topic rather stay stress-free, relaxed and calm while answering the questions.