What is the greatest integer m for which the number 50!/14^m is an integer?  Choose the correct option:
A) 11  B) 10  C) 9  D) 8  E) 7
14^m = 2^m*7^m.   Let's figure out how many 7's are in the prime factorization of 50!   The multiples of 7 are: 7, 14, 21, 28, 35, 42, 7*7.   Thus 7^8 will divide 50! but 7^9 will not.   Clearly 2^8 will divide 50!   So m=8 is the largest possible integer.   The answer is 8.
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What is the greatest integer m for which the number 50!/14^m is an integer?