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(Assuming a three digit number is in the range 100-999 and excludes leading zeros, that is 080 does not count as it is really 80 which is a two digit number)

To be divisible by 11, the difference in the sums of the alternate digits of the number must be divisible by 11 (or 0).

For a three digit number, this means that the sum of the first and last digits less the second digit must be a multiple of 11 (or 0).

For a three digit number with all the digits the same, this calculation results in the value of one of the digits (eg 333 → 3 + 3 - 3 = 3) which will not be 0, and cannot be a multiple of 11 as a single digit is less than or equal to 9 which is less than 11 and thus not a multiple of 11.

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โˆ™ 2012-02-16 08:35:07
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Q: When a three digit number has the same three numbers is it divisible by 11?
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