Factorials and Trailing Zeroes

23! has four trailing zeroes

101! has 24 trailing zeroes

1000! has 249 trailing zeroes

4617! has 1151 trailing zeroes.

http://www.purplemath.com/modules/factzero.htm

Note that 41! = 33452526613163807108170062053440751665152000000000

It is a 50 digits long, the last 9 of them are 0s. So the trailing zeros represent 18%

Find n where n! has the largest possible proportion of trailing 0s.