# How do I find if a number is a multiple of 8?

Apr 4, 2016

Please see the process and reason below.

#### Explanation:

Just check the last three digits of the number.

If they are divisible by $8$, the entire number is divisible by $8$.

For example, last three digits of $53927592$ are $592$ and they are divisible by $8$ as $592 = 74 \times 8$.

Hence, $53927592$ is divisible by $8$ and $53927592 = 6740949 \times 8$.

The reason is that as the number can be expressed as
$Y Y Y Y Y Z Z Z = Y Y Y Y Y \times 1000 + Z Z Z$

= $Y Y Y Y Y \times 125 \times 8 + Z Z Z$.

As $Y Y Y Y Y \times 125 \times 8$ is divisible by $8$, if $Z Z Z$ is divisible by $8$, $Y Y Y Y Y Z Z Z$ is divisible by $8$.