__maths__>__Divisibility in Whole Numbers__>__Simple Divisibility Tests: 2, 10, 3, 4, 5, 11, 9, 6__### Divisibility by 11

In this page, a simple overview of the divisibility test for `11` is provided.

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Which of the following are multiples of `11`?

- `11,22,33, cdots, 110,121,132, cdots`
- `10,20,30,40,cdots`
- `10,20,30,40,cdots`

The answer is "`11,22,33, cdots, 110,121,132, cdots`"

Consider the multiples of `11` given as `11,22,33, cdots, 110,121,132, cdots`. Is there any similarity observed in the multiples? Note: A number `3521` when multiplied by `11` is given as

`3521 xx 11`

`=3521 xx(10+1)`

`=35210+ 3521`

`=(3)(5+3)(2+5)(1+2)(1)`

Four digit number, when multiplied by `11`, results in

• units digit of product is same as that of multiplicand

• tens digit of product is sum of units and tens digit of multiplicand

• hundreds digit of product is sum of tens and hundreds digit of multiplicand

• and so on.

- alternate digits have some pattern
- there is no similarity observed
- there is no similarity observed

The answer is "alternate digits have some pattern".

Consider `121` and `125`. Which of these is divisible by `11`?

Check this by long division method.

- `121`
- `121`
- `125`
- both the above

The answer is "`121`".

The multiples of `11` have the property explained below. For example, consider `121` (a multiple of `11`).

Add the digits in odd positions `1+1`, the result is `2`

Add the digits in even positions `2`.

Find the difference between these two results.

If the difference is `0` or a multiple of `11`, then the number is a divisible by `11`.

**Test for Divisibility by 11** : Find the sum of digits in even positions and the sum of digits in odd positions. If the difference between these two sums is a multiple of 11, then the number is divisible by 11.

Is `2108` divisible by `11`?

- Yes
- No
- No

The answer is "No". The sum of alternate digits are `2+0=2` and `1+8=9`. The difference between these sums are `9-2 = 7`. Since `7` is not divisible by `11`, the number is not divisible by `11`.

Is `902` divisible by `11`?

- Yes
- Yes
- No

The answer is "Yes". The `9+2-0 = 11`, so the number is divisible by `11`.

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