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