If p is the product of the integers from 1 to 35, inclusive, what is the greatest integer k for which 3^k is a factor of p?
Pick one: A) 11 B) 13 C) 15 D) 17 E) 19

Rationale: "35 ! 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