What is the greatest integer m for which the number 40!/14^m is an integer?	Choose the correct choice from the following answers.
A) 8  B) 7  C) 6  D) 5  E) 4
14^m = 2^m*7^m.   Let's figure out how many 7's are in the prime factorization of 40!   The multiples of 7 are: 7, 14, 21, 28, 35.   Thus 7^5 will divide 40! but 7^6 will not.   Clearly 2^5 will divide 40!   So m=5 is the largest possible integer.   The answer is 5.
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What is the greatest integer m for which the number 40!/14^m is an integer?