# (n-1)! is divisible by n

by xax
Tags: divisible
 P: 26 I need to prove this for any n natural, n>= 5, n not prime.
 P: 688 Think a bit about the prime factors of n... are they smaller than n? Then think of what (n-1)! means.
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,877 Dodo's hint is excellent- but the crucial point is whether the factors of n are less than n-1, not jus n itself!
 P: 39 Sorry, xax but I don't really understand your idea heh. This is how I see it: $$n > 4$$ implies that $$\sqrt{n} > 2$$ so we also have that $$\sqrt{n}\sqrt{n} > 2\sqrt{n}$$ or simply $$n > 2\sqrt{n}$$, meaning that $$2\sqrt{n}$$ and $$\sqrt{n}$$ both show up in $$(n-1)!$$ so we're good to go.