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 correct option:	A) 10	B) 12	C) 14	D) 16	E) 18
W = 30!   8   W = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1   Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3   3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3   So we have a total of 14 three's ...   Therefore the maximum value of K can be 14 (14)
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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?