What is the greatest integer m for which the number 30!/10^m is an integer?	Select
A) 7 B) 8 C) 9 D) 10 E) 11
10^m = 2^m*5^m.   Let's figure out how many 5's are in the prime factorization of 30!   The multiples of 5 are: 5, 10, 15, 20, 5*5, 30.   Thus 5^7 will divide 30! but 5^8 will not.   Clearly 2^7 will divide 30!   So m=7 is the largest possible integer.   The answer is 7.
<result>A</result>
What is the greatest integer m for which the number 30!/10^m is an integer?