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There are 57 trailing zeros in 238!.

There is an easy way to figure this :

First......divide 238 by 5   and forget any remainders  =   47

Next.......divide 238 by 25 and forget any remainders = 9

Next......divide 238 by 125 and forget any remainders  = 1

Add the three numbers =  47 + 9 + 1 =   57 traliing zeroes.....just as Guest said......