If e 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 e ? Choose the correct choice.
A) 10
B) 12
C) 14
D) 16
E) 18
Answer is C.   numbers in format of 3^k in the series from 1 to 30 inclusive e 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.
<result>C</result>
If e 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 e ?