If p is the product of the integers from 1 to 34, inclusive, what is the greatest integer k for which 3^k is a factor of p? Choose the correct choice from the following answers:
A) 11
B) 13
C) 15
D) 17
E) 19

Rationale: 34 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c .
Answer: C