Counting zeroes

Find the number of trailing zeroes of ( 100 ! ) (100!) .

24 22 25 23

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1 solution

Hari Om Sharma
Aug 15, 2015

The number of zeroes is = number of 10's = exponent of 2 X exponent of 5 exponent of 2 = [100/2] + [100/4] +[100/8] +[100/16 ] +[100/32] +[100/64] = 97 exponent of 5 = [100/5] + [100/25] = 24 Hence exponent of 10 = min( 97,24) = 24

NOTE : Here [ * ] means greatest integer function.

if alternate easy solution is available then share.

Moderator note:

Simple standard approach to calculate the number of trailing zeros in a factorial.

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