I am not sure whether approximations are OK for your case. But if it is, have you thought about Stirling's approx and Gosper's approx for factorials?

http://mathworld.wolfram.com/StirlingsApproximation.html

-SK

In reply to Re^5: Algorithm for cancelling common factors between two lists of multiplicands by sk
in thread Algorithm for cancelling common factors between two lists of multiplicands by BrowserUk

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