__maths__>__Divisibility in Whole Numbers__>__Simplification of Divisibility Tests: 8, 12, 15__### Divisibility by 8

In this page, a simple overview of the divisibility test for `8` is provided. The procedure uses simplification by subtraction.

*click on the content to continue..*

Consider `1000` and `224`. Which of these is divisible by `8`?

Check this by long division method.

- `1000`
- `224`
- both the above
- both the above

The answer is "both `1000` and `224`"

The multiples of `8` have the property that lowest `3` digits (hundreds, tens and units) is divisible by `8`.*Explanation for the curious mind*

A large number `2344` can be given in the form `2xx1000+344`.

It is learned that if one addend is divisible, then the divisibility test can be performed only on the second addend.

`2xx1000` is divisible by `8` as `1000=125xx8`.

So the divisibility test is performed on `344`, that is the last `3` digits of the number.

**Test for Divisibility by `8`** : If the last three digits of the dividend is divisible by `8`, then the dividend is divisible by `8`.

Is `2018` divisible by `8`?

- Yes
- No
- No

The answer is "No". Checking the last three digits `18`. As `18` is not a multiple of `8`, it is concluded that the number is not divisible by `8`.

Is `7120` divisible by `8`?

- Yes
- Yes
- No

The answer is "Yes". Checking the last three digits `120`. As `120` is a multiple of `8`, it is concluded that the number is divisible by `8`.

Is `73524` divisible by `8`?

- Yes
- No
- No

The answer is "No". Checking the last three digits `524`. The divisibility test can be simplified by subtraction (`524-400-80-40`) or simplified by factors (`(524,8)` simplified to `(262,4)`, then to `(131,2)`).

*slide-show version coming soon*