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

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Intern
Joined: 11 Jul 2008
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If p is the product of the integers from 1 to 30, inclusive, [#permalink]

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01 Oct 2008, 20:56
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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 3^k is a factor of p?

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

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Manager
Joined: 30 Sep 2008
Posts: 111

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01 Oct 2008, 21:12
From 1 to 3, the integers are divisible by 3^n (n>=1):

By 3: 3, 6, 12, 15, 21, 24, 30 <--7
By 3^2: 9, 18 <-- 2 x 2 = 4
By 3^3: 27 <- 1 x 3 = 3

Total 7 + 4 + 3 = 14 = k

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SVP
Joined: 07 Nov 2007
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Location: New York

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01 Oct 2008, 21:13
xang 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 + (30/3^2) nearest integer(floor) + 30/3^3 nearest integer(floor)
= 10+3+1
=14
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VP
Joined: 17 Jun 2008
Posts: 1374

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01 Oct 2008, 21:22
xang 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

IMO C
count the number of threes in the numbers 1-30 inclusive ,14 is the answer
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Re: PS -   [#permalink] 01 Oct 2008, 21:22
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