If w 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 w ?
Choose the most appropriate option: 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 w 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 w 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 w ?