Is it easier to calculate a factorial or the inverse of a factorial (1/n!) for extremely large n?

Is it easier to calculate a factorial or the inverse of a factorial (1/n!)
for extremely large n?

I need to calculate extremely large factorials but they grow extremely
fast! I was wondering if it might be easier to calculate $\frac{1}{n!}$
rather than n! itself because as n goes to infinity $\frac{1}{n!}$ goes to
zero, which I think may be easier to calculate. Is it easier to calculate
the factorial or the inverse of it?