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# If p is the product of the integers from 1 to 30, inclusive,

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Joined: 15 Oct 2007
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If p is the product of the integers from 1 to 30, inclusive, [#permalink]  17 Oct 2007, 00:53
If p 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 p?

A. 10
B. 12
C. 14
D. 16
E. 18
VP
Joined: 09 Jul 2007
Posts: 1108
Location: London
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Re: Factor Q [#permalink]  17 Oct 2007, 02:18
mistahfold wrote:
If p 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 p?

A. 10
B. 12
C. 14
D. 16
E. 18

it is 30!
1*2*3*4*....27*28*29*30

there are 10 integers divisible by 3 (30/3=10)

3,3*2,3*3,3*4,3*5...3*3*3,10*3

14 C
Director
Joined: 03 May 2007
Posts: 894
Schools: University of Chicago, Wharton School
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Re: Factor Q [#permalink]  17 Oct 2007, 06:34
mistahfold wrote:
If p 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 p?

A. 10
B. 12
C. 14
D. 16
E. 18

30/3 = 10
30/9 = 3
30/27 = 1
sum = 14

so C.
Re: Factor Q   [#permalink] 17 Oct 2007, 06:34
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