# Digit sums of multiples of 11

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Some multiples of 11 have an even digit sum.
For example-
7*11 = 77 and 7+7 = 14, which is even;
11*11 = 121 and 1+2+1 = 4, which is even.

Do all multiples of 11 have an even digit sum?
(Prove that they do or find the smallest that does not.)

ronret45 Expert Asked on 1st August 2015 in

using 11 division test we know abcdef if divisible by 11
a + c+e+(b+d+f)=2(sum of even or odd places) + some multiple of  11 having less digits then abcdef.now suppose statement in question works till n digits where n is any number then it will work for n+1 digits we just prove it works when n =2  so i did it

Yodha Expert Answered on 4th April 2016.

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