What is the greatest integer m for which the number 40!/14^m is an integer?  Choose the correct choice from the following:
A) 8
B) 7
C) 6
D) 5
E) 4

Rationale: 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 d .
Answer: D