Let us find those numbers which exactly divide 6. Clearly, 6 is not exactly divisible by any number greater than 6. So, let us divide 6 by any number less than or equal to 6.

We have, 6 ÷ 1 = 6 so, quotient = 6 and remainder = 0.Therefore, 6 = 1 × 6

Again 6 ÷ 2 = 3 so, quotient = 3 and remainder = 0.Therefore, 6 = 2 × 3

Similarly again, 6 ÷ 3 = 2 so, quotient = 2 and remainder = 0.Therefore, 6 = 3 × 2

From this we observe that 1, 2, 3 and 6 are exact divisors of 6.These numbers are called factors of 6.

Thus, we can define the term factor as follows,

**A factor of a number is an exact divisor of that number.**

In other words, a factor of a number is that number which completely divides the number without leaving a remainder.

Each of the numbers 1, 2, 3, 4, 6 and 12 is a factor of 12. However, none of the numbers 5, 7, 8, 9,10 and 11 is a factor of 12.

For example, 8 divides 40 exactly, therefore 8 is a factor of 40. Similarly, 4 is a factor of 16 and 5 is a factor of 25.

Observe the following:

**Multiples**

A multiple of a number is a number obtained by multiplying it by a natural number.

If we multiply 3 by 1, 2, 3, 4, 5, 6... ,we get

3 × 1 = 3, 3 × 2 = 6, 3 × 3 = 9, 3 × 4 = 12, 3 × 5 = 15, 3 × 6 = 18 ...

Thus, 3, 6, 9, 12, 15, 18 ... are multiples of 3

Clearly, a number is a multiple of each of its factors.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28...

Each of these multiples is greater than or equal to 4.

1 is the common factor of every number and every number is always a factor of itself. 1 is the only number which has exactly one factor, so it is a unique number.