There are 24 factors of 5 in 100!: one for each multiple of 5 in [1,100] and one more for each multiple of 5*5.

There are >50 factors of 2 in 100!: one for each multiple of 2, one for each multiple of 2*2, one for each multiple of 2*2*2, etc.

So, there are 24 factors of 10 in 100! since 10=2*5.

So there are 24 zeros on the end of 100!, since each zero on the end implies a factor of 10.

--Glenn

P.S.: I got it wrong in my head when I implied it was 21.
P.P.S.: Anyone want the shortcut answer to "N balls in M bins?"