Posted by Brenda on Thursday, January 10, 2013 at 9:37pm.
For how many positive integers n does n! end in exactly 5 0s?

math  Reiny, Thursday, January 10, 2013 at 10:26pm
we get a zero when we multiply be a number ending in either 2 and 5 or a 10
at the end of 5!  one zero
at the end of 10!  two zeros
at the end of 15!  3 zeros
at the end of 20!  4 zeros
at the end of 25!  5 zeros
e.g.
10! = 10x9x8x7x6x5x5x3x2x1
= 2x5x3x3x2x2x2x7x3x2x5x2x2x3x2
= (2^8 x 5^2) x 3^4 x 7
= 6400 x 567  ending in 2 zeros