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example 3. Is 382 a multiple of 18?

Solution. If 382 is a multiple of 18, then it should be completely divisible by 18.

By long division: 2 1

18 3 8 2
– 3 6

2 2
– 1 8
4

Here, the remainder is 4 and not 0, so 382 is not completely divisible by 18.

Thus, 382 is not a multiple of 18.

Properties of Multiples

1. Every number is a multiple of itself.

For example, 3 = 3 × 1, 8 = 8 × 1, 25 = 25 × 1, etc.

2. Every number is a multiple of 1.

For example, 3 = 1 × 3, 5 = 1 × 5, 15 = 1 × 15, etc.
3. Every multiple of a given number is greater than or equal to that number.

For example, multiples of 3 are 3, 6, 9, 12, ...

4. There are an infinite number of multiples of a number.

For example, multiples of 5 are 5, 10, 15, 20, 25, 30 and so on.

Factors

If a number can divide a bigger number exactly, that is, without leaving any remainder,
then we say that the smaller number is a factor of the bigger number.
Let us consider a number, say 24, and divide it by all the possible numbers.

We know that:

24 ÷ 1 = 24 24 ÷ 2 = 12 24 ÷ 3 = 8, 24 ÷ 4 = 6

24 ÷ 6 = 4 24 ÷ 8 = 3 24 ÷ 12 = 2 24 ÷ 24 = 1

We observe that 24 is completely divisible by 1, 2, 3, 4, 6, 8, 12 and 24.
Thus, the numbers 1, 2, 3, 4, 6, 8, 12 and 24 are all factors of 24.

The factors of a number can be found either by multiplication or by division.

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Multiples and Factors