__maths__>__Divisibility in Whole Numbers__>__Classification of Numbers based on Remainder in Division: Odd-Even and Prime-Composite__### Divisibility of a Dividend by a Divisor

In this page, the concept of divisibility is introduced with simple examples.

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What is `5-:2`?

- only `2`
- quotient `2` and remainder `1`
- quotient `2` and remainder `1`
- both the above

The answer is "quotient `2` and remainder `1`".

What is `6-:2`?

- only `3`
- quotient `3` and remainder `0`
- both the above
- both the above

The answer is "both the above".

Note the difference

• Result of `6-:2` is, quotient `3` and remainder `0`.

• Result of `5-:2` is, quotient `2` and remainder `1`

For a given divisor, the numbers can be grouped as

• numbers for which remainder is `0` and

• numbers for which remainder is not `0`.

A number is called "**divisible**" by a divisor, if the remainder is `0`.

Which of the following is a meaning for the word "divisible"?

- having capability to be divided with `0` remainder
- having capability to be divided with `0` remainder
- having capability to change from one activity to another

The answer is "having capability to be divided with `0` remainder".

What is the term used to refer "a number can be divided without remainder"?

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is "divisible".

**Divisibility** : A number (dividend) is divisible by a divisor number if the remainder is `0`.

Is `42` divisible by `8`?

- Yes
- No
- No

The answer is "No". `42-:8 = 5 text( quotient ) 2 text( remainder )`. So `42` is not divisible by `8`.

Is `12` divisible by `6`?

- Yes
- Yes
- No

The answer is "Yes". `12-:6 = 3 text( quotient ) 0 text( remainder )`. So `12` is divisible by `6`.

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