If r is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of r ?
Choose the most appropriate option: A) 10 B) 12 C) 14 D) 16 E) 18

Rationale: answer is c . numbers in format of 3 ^ k in the series from 1 to 30 inclusive r are : 3 * 1 , 3 * 2 , 3 * 3 , 3 * 4 , 3 * 5 , 3 * 3 * 2 , 3 * 7 , 3 * 8 , 3 * 3 * 3 , 3 * 10 . total number of 3 = 13 . so k = 14 .
Answer: C