# Mathematics - Class 6 / Grade 6

- Playing With Numbers – Factors and Multiples
### Playing With Numbers – Factors and Multiples

Tags: Factors and Multiples Notes and Lesson for class 6, Factor and Multiples free printable Worksheets PDF with answers for 6th class, Practice page, examples and exercise on factors and multiples for sixth grade, what are factors? What are multiples? Playing with numbers – Factors and Multiples for grade 6, Write all the factors of 15, 22, 36 and 45. Write next 4 multiple of 10, 12, 16 and 22, Number that has exactly only 1 factor, Can there be any natural number that does not have factor at all? Find all the multiple of 13 up to 100. Write all the factors of 120. Find the missing factors. Write the multiples of 8 which are greater than 30 and less than 80. Circle the numbers below which are factors of 65. Write all the possible factors of 38. 1 is a factor of every number; Every number is a multiple of itself. Every multiple of a number is greater than or equal to the given number. Number of multiples of a given number is infinite. Number of factors of a given number is finite. Every factor of a number is an exact divisor of given number. Every factor is less than or equal to the given number.### Factors and Multiples

#### Factors

Let’s start with division of 6. We can divide the given number by a number less than or equal to the given number.

So, number 6 can be written as:

6 = 1 × 6;

6 = 2 × 3;

6 = 3 × 2;

6 = 6 × 1;

Therefore numbers 1, 2, 3 and 6 are exact divisors of 6.

__These numbers are called factors of 6.__So, factors are what we can multiply to get the number.

Or we can say, numbers that divides a given number completely i.e., without leaving remainder is called a factor of the given number. A factor is also called a

__divisor__. A number can have**many**factors.#### Multiples

Example:

6 = 2 x 3

8 = 2 x 4

From the above example we conclude that a multiple is the product of a number and an integer.

__Let’s find out the multiple of 2.__2 x 1 = 2

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8 and so on

Therefore, multiple of 2 are obtained by multiplying it by a natural number.

#### Facts about Factors and Multiples

#### 1. 1 is a factor of every number. Example: 5 = 1 × 5, 9 = 1 × 9 and so on

#### 2. Every number is a factor of itself. Example: We can write 12 as 12 = 12 × 1.

#### 3. Every factor of a number is an exact divisor of given number. Example: Factors of 8 are 1, 2, 4 and 8. So, 1, 2, 4 and 8 are exact divisor of 8.

#### 4. Every factor is less than or equal to the given number. Example: Factor of 34 are 1, 2, 17 1nd 34 itself.

#### 5. Number of factors of a given number is finite. We can count the number of factors of even larger numbers.

#### 6. Every multiple of a number is greater than or equal to the given number. Example: Multiple of 3 are 3, 6, 9, 12, 15…

#### 7. Number of multiples of a given number is infinite. Example: Multiple of 2 are 2, 4, 6, 8, 12, 15 …… The list is endless.

#### 8. Every number is a multiple of itself. Example: 6 = 6×1.

#### 9. A number for which sum of all its factors is equal to twice the number is called a perfect number.

Example: Factors of 6 are 1, 2, 3 and 6.

Sum of all its factors = 1+2+3+6 = 12

12 = 2 × 6 (sum = 2 of the number)

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