Seems to me that this problem requires you to factor numbers. Factoring numbers is considered to be a really hard problem - it's what public key encryption makes secure. Noone knows a fast way to factor numbers (well, maybe someone does, but then, they have kept it a secret), so if you are going to have big numbers, the factoring will be the bottleneck.
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Re^2: Algorithm for cancelling common factors between two lists of multiplicands
by BrowserUk (Pope) on Aug 09, 2005 at 13:41 UTC