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Tests for Divisibility of Numbers - Divisibility by 11

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Divisibility by 11:

To check the divisibility of a number by 11, the rule is, find the difference between the sum of the digits at odd places (from the right)and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.

Number

Sum of the digits (at odd places) from the right

Sum of the digit (at even places) from the right

Difference

308

8 + 3 = 11

0

11 – 0 = 11

1331

1 + 3 = 4

3 + 1 = 4

4 – 4 = 0

61809

9 + 8 + 6 = 23

0 + 1 = 1

23 – 1 = 22

We observe that in each case the difference is either 0 or divisible by 11. All these numbers are also divisible by 11.

For the number 5081, the difference of the digits is (5+ 8) – (1 + 0) = 12which is not divisible by 11. The number 5081 is also not divisible by 11.

More Examples:

Is the number 2547039 divisible by 11?
First, find the difference between the sum of its digits at odd and even places.
(Sum of digits at odd places) - (Sum of digits at even places)
= (9 + 0 + 4 + 2) - (3 + 7 + 5)
= 15 - 15 = 0
The number is 0, so the number 2547039 is divisible by 11.

Is the number 13165648 divisible by 11?
(Sum of digits at odd places) - (Sum of digits at even places)
= (8 + 6 + 6 + 3) - (4 + 5 + 1 + 1)
= 23 - 11 = 12
The number is 12, so the number 13165648 is not divisible by 11.

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