http://www.perlmonks.org?node_id=482192


in reply to Algorithm for cancelling common factors between two lists of multiplicands

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.