Instead of actually carrying out a division, it is possible to "test" a number to see if it can be divided exactly by certain numbers.

If a number divides exactly into a number, it is divisible by this number.

24 is divisible by 2, because 24 ÷ 2 is a whole number.

24 is not divisible by 5, because 24 ÷ 5 is not a whole number.

Here are the rules to test divisibility by 2, 3, 5 and 10.

__Rule for 2__

A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8.

This means that it is even.

__Rule for 3__

A number is divisible by 3 if the sum of its digits is divisible by 3

3045 is divisible by 3, because 3 + 0 + 4 + 5 = 12 which is divisible by 3

3044 is therefore not divisible by 3, because 11 is not divisible by 3.

**Rule for 5**

A number is divisible by 5 if it ends in 0 or 5.

3045 is divisible by 5, because it ends in 5.

3030 is divisible by 5, because it ends in 0.

5551 is not divisible by 5.

**Rule for 10**

A number is divisible by 10 if it ends in 0.

3140 is divisible by 10, because it ends in 0.

3145 is not divisible by 10.

**Example1**

What digit must replace the ?, to make the number 501? divisible by 5?

**Answer**

? can be 0 or 5.

**Example 2**

What digit must replace the ?, to make the number 501?2 divisible by 3?

**Answer**

So far, 5 + 0 + 1 + 2 = 8

this means that ? could equal 1, 4 or 7 to give a digit sum of 9, 12 or 15.