Without performing the actual division, determine whether 11298969 (base ten) is divisible by 2013 (base ten).

You can easily check that both are divisible by both 3 and 11.  Dividing 2013 by 33 gives 61.

Unfortunately I don't know an easy way to test divisibility by 61.

Is it cheating to do just this division?  11298969/61 = 185229

So yes.

An more straightforward wary would be to just look at the prime factorization of each I suppose:
11298969 = 3^2 * 11 * 61 * 1871
2013 = 3 * 11 * 61
which also shows it is divisible.

Posted by Jer on 2011-11-29 13:55:03