What is the greatest integer m for which the number 40!/10^m is an integer? Choose the correct option
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 40!   The multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35, 40.   Thus 5^9 will divide 40! but 5^10 will not.   Clearly 2^9 will divide 40!   So m=9 is the largest possible integer.   The answer is 9.
<result>C</result>
What is the greatest integer m for which the number 40!/10^m is an integer?