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If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3k is a factor of p ? (A) 10 (B) 12 (C) 14 (D) 16 (E) 18

Re: If p is the product of the integers from 1 to 30, inclusive [#permalink]

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01 Oct 2012, 05:50

P = 30! 8 P = 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 (C)
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