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2014-09-07T12:24:10+05:30

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Let that digit be a.
a a a a a a = a(10^5+10^4+10^3+10^2+10+1) = 111111 * a \\ \\ Sum\ of\ alternate\ digits\ in\ 111111\ is\ 3.\ \ It\ is\ divisible\ by\ 11.\ \\ \\ sum\ of\ digits\ is\ 6.\ So,\ divisible\ by\ 3.

aaaaaa = a * 111111 = a * 3 * 11 * 3367 = a * 3 * 11 * 13* 259
111111 is divisible by 13. So all those number are divisible by 13.

another simpler method: divisibility by 13

111111 => 11111+1*4 = 11115 => 1111 + 5*4 = 1131 => 113 + 1*4 = 117 = 9 * 13
So 111111 is divisible by 13 and so aaaaaa is also divisible.

6 4 6
2014-09-07T14:46:01+05:30
555555/15=37037
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answer is fine

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