Identifying the Multiples of 3 and 6

Multiples of 3

We can recognise easily whether a number is a multiple of 3 by using the following rule.

If the sum of the digits of a number is a multiple of 3, then the number must also a multiple of 3.

For example:

Is 432 a multiple of 3?

The sum of the digits:

4 + 3 + 2 = 9

and nine is a multiple of 3. Therefore 432 is a multiple of 3.

Let's see another example:

Is 8572534 a multiple of 3?

The sum of the digits:

8 + 5 + 7 + 2 + 5 + 3 + 4 = 34

and 34 is not a multiple of 3. Therefore 8572534 is not a multiple of 3.

Multiples of 6

6 is a multiple of 2 and 3. Therefore, we can tell whether a number is a multiple of 6 by using the following rule:

If a number is an even number and divisible by 3, then the number is a multiple of 6.

For example:

Is 4632 a multiple of 6?

The sum of the digits:

4 + 6 + 3 +2 = 15

and 15 is divisible by 3 (because it is a multiple of 3).

Also, 4632 is an even number (hence it is divisible by 2).

Therefore, 4632 is divisible by 6

Let's see another example:

Is 97626 a multiple of 6?

First, it is an even number.

And the sum of the digits:

9 + 7 + 6 + 2 + 6 = 30

30 is divisible by 3, hence 97626 is divisible by 6.