Saturday, March 5, 2011

Factorials and Trailing Zeroes

23! has four trailing zeroes

101! has 24 trailing zeroes

1000! has 249 trailing zeroes

4617! has 1151 trailing zeroes.




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.

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