 ## Factors and Multiples

### Factors

A set of numbers which divides a particular number without leaving any remainder is called the factors of that particular number. For example 1, 2, 3, 4, 6 and 12 can divide 12 without leaving any remainder, so 1, 2, 3, 4, 6 and 12 are the factors of 12.
12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1
We write this set of numbers in symbolic form as given below.
F12 = {1, 2, 3, 4, 6, 12}

### Multiples

Multiples of a number are the set of numbers which are obtained by multiplying the number with the whole numbers. For example 0, 3, 6, 9, 12, 15, 18, … are the the set of multiples of 3.
3 × 0 = 0
3 × 1 = 3
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12 and so on.
We write this set of numbers in symbolic form as given below.
M3 = {0, 3, 6, 9, 12, 15, 18, …}

### Workout Examples

Example 1: Find the factors of 18.

Solution: Here,
Factors of 18 are 1,2,3,6,9 and 18.
F18 = {1, 2, 3, 6, 9, 18}

Example 2: Find the multiples of 4 up to 20.

Solution: Here,
Multiples of 4 up to 20 are 0, 4, 8, 12, 16 and 20.
M4 = {0, 4, 8, 12, 16, 20}

Example 3: Write the common factors of 12 and 16.

Solution: Here,
Factors of 12, F12 = {1, 2, 3, 4, 6, 12}
Factors of 16, F16 = {1, 2, 4, 8, 16}
Common factors of 12 and 16 = {1, 2, 4}

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