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December 19, 2014

December 19, 2014

Posted by **Anonymous** on Wednesday, June 24, 2009 at 1:48pm.

- Math -
**Count Iblis**, Wednesday, June 24, 2009 at 2:06pmDenote your number by N. Suppose N is divisible by M. So, we have:

N = M Y

where Y is another integer. Then, M is also divisible by Y. If we are testing different numbers starting from small to large, then it is not possible for Y to be smaller than M, because then you should have encountered the divisor Y already.

This means that you don't have to test numbers M for which

N/M < M ------->

M^2 > N --------->

M > sqrt(N)

So, we only need to test numbers smaller than or equal to the square root of N.

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