Divisibility Rule of 11: Rule, Examples
Divisibility Rule of 11
A number is divisible by 11 if the difference between the sum of its digits in odd places and the sum of its digits in even places is a multiple of 11 (including 0).
If the result is 0, 11, 22, 33, or any multiple of 11, then the number is divisible by 11.
Steps to Check Divisibility by 11
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Write down the number.
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Find the sum of the digits in odd places (from right to left).
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Find the sum of the digits in even places (from right to left).
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Subtract the two sums.
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If the answer is 0 or a multiple of 11, then the number is divisible by 11.
Examples
Example 1: Is 2728 divisible by 11?
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Number: 2728
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Digits in odd places: 8 and 7 -> 8 + 7 = 15
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Digits in even places: 2 and 2 -> 2 + 2 = 4
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Subtract the sums: 15 - 4 = 11
2728 is divisible by 11.
Example 2: Is 31415 divisible by 11?
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Number: 31415
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Digits in odd places: 5, 4, 3 -> 5 + 4 + 3 = 12
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Digits in even places: 1 and 1 -> 1 + 1 = 2
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Subtract the sums: 12 - 2 = 10
31415 is not divisible by 11.
Know the divisibility rule of 15 here.
Try It Yourself:
Are they divisible by 11?
1. 7986
2. 4532
3. 90909
FAQs
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What is the divisibility of 11 with example?
According to the divisibility test of 11, the difference of the sum of digits at odd places and the sum of digits at even places should be 0 or 11 for the given number 3784, to be divisible completely by 11. The sum of digits placed at an odd position in the number 3784 is 11 (3 + 8 = 11).
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Is 764852 divisible by 11?
The difference between the sum of digits at odd and even place = 16 – 16, which is 0. Hence, 764852 is divisible by 11.
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What is the divisibility rule of 11?
A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11. To apply this rule, start by numbering the digits from right to left, with 1 being the first digit, 2 the second, and so on. Then, sum the digits in odd positions and sum the digits in even positions. Finally, subtract the sum of the even digits from the sum of the odd digits. If the result is 0 or a multiple of 11, the original number is divisible by 11.