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

In this page, Simplification of divisibility test by subtraction is explained. This is used to develop other divisibility tests for specific numbers.

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Given a number `83xx2322 = 192726`. is it divisible by `83`?

- Yes
- Yes
- No
- Can't say

The answer is "Yes". The number is given as a multiple of `83`, so it is divisible by `83`.

Consider a number `83xx23 + 422 = 2331`, Which of the following helps to find if the number is divisible by `83`?

- we have to check the large number `2331`
- we can check the smaller number `422` which is easier
- we can check the smaller number `422` which is easier

The answer is "we can check the smaller number `422` which is easier".

Consider a number `2331`, Which of the following helps to find if it is divisible by `83`?

- we have to check the large number `2331`
- it can be simplified to a smaller number `2331-83xx20=671` which is easier
- it can be simplified to a smaller number `2331-83xx20=671` which is easier

The answer is "It can be simplified to a smaller number".

To check the divisibility, the following properties are helpful.

• multiple of a number is divisible by the number.

eg: `3xx423` is a multiple of `3` and so it is divisible by `3`.

• In a sum of two numbers, if one number is a multiple of the divisor, then only the other number is checked for divisibility.

eg: Divisibility test of `3xx423 + 7` by `3`, can be simplified to divisibility test of `7`, as `3xx423` is a multiple of `3`.

• To check divisibility of a large number by a divisor, it can be simplified into a smaller number by subtracting a multiple of the divisor.

eg: Divisibility test of `913` by `3`, can be simplified to divisibility test of `913-300xx3 = 13`

The method is named **Simplification by Subtraction** method.

**Simplification by Subtraction for Divisibility Tests**: To perform divisibility test on a large number, a multiple of a divisor can be subtracted and the divisibility test is performed on the difference.

Find the divisibility of `777012` by `111`.

- Not Divisible. Subtract `777012 - 111xx7000 = 12`. Check the divisibility on `12`
- Not Divisible. Subtract `777012 - 111xx7000 = 12`. Check the divisibility on `12`
- It is not simple to check divisibility large numbers

The answer is "Not Divisible"

Find the divisibility of `804` by `67`.

- Not Divisible. Subtract `804 - 67xx10 = 134`. Check the divisibility on `134`
- Divisible. `134=67xx2` is divisible by `67`
- Divisible. `134=67xx2` is divisible by `67`

The answer is "Divisible"

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