There is a one number which is formed by writing one digit 6 times eg 111111 555555 etc such a numbe...........

Quantitative Aptitude ( CCS) Number System

There is a one number which is formed by writing one digit 6 times (eg.111111,555555,...etc.). such a number is always divisible by:

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Explanation:

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.