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

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

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05 Aug 2008, 08:29
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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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05 Aug 2008, 08:32
C.

Essentially this is asking you to break down 30! into it's prime roots and count the 3s. I think I counted them all
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Intern Joined: 22 Jul 2008 Posts: 45 Followers: 0 Kudos [?]: 14 [0], given: 0 Re: Factor question [#permalink] Show Tags 05 Aug 2008, 08:35 Can you further explain your reply. Are u refereing to factors of 30 or 30!(factorial) IF it is 30! how would you get the 3's Senior Manager Joined: 23 May 2006 Posts: 325 Followers: 2 Kudos [?]: 329 [1] , given: 0 Re: Factor question [#permalink] Show Tags 05 Aug 2008, 08:37 1 This post received KUDOS Agree. IMO C as well take the (3's in) 3,6,9,12,15,18,21,24,27,30 You will find that there are 14 3's SVP Joined: 30 Apr 2008 Posts: 1874 Location: Oklahoma City Schools: Hard Knocks Followers: 42 Kudos [?]: 590 [0], given: 32 Re: Factor question [#permalink] Show Tags 05 Aug 2008, 08:39 "If p is the product of the integers from 1 to 30, that's 1 * 2 * 3 * 4 ...28 * 29 * 30. 30! is written 30 * 29 * 28 * 27...1. This is the same thing but written in different ways. How i did it is I started at 1. and counted up and for each integer I counted how many times you can divide 3 into that number. 1 = 0 2 = 0 3 = 1 (3 is prime) 4 = 0 5 = 0 6 = 1 (3*2) 7 = 0 8 = 0 9 = 2 (3*3) 10 = 0 11 = 0 12 = 1 (3*2*2) 13 = 0 14 = 0 15 = 1 (3*5) 16 = 0 17 = 0 18 = 2 (3*3*2) 19 = 0 20 = 0 21 = 1 (3*7) 22 = 0 23 = 0 24 = 1 (3*2*2*2) 25 = 0 26 = 0 27 = 3 (3*3*3) 28 = 0 29 = 0 30 = 1 (3*2*5) rnemani wrote: If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p? A. 10 B. 12 C. 14 D. 16 E. 18 _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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05 Aug 2008, 10:52
rnemani 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

max n 3 ^n less than 30 n=3

greatest integer k for which 3^k is a factor of p
= (30/3) + (30/3^2)~(integer) + (30/3^3)~integer
= 10+3+1
=14
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05 Aug 2008, 17:55
rnemani 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

simple getting the number of multiples if 3 in 30 => 10 multiples here
hence 10 is the k which becomes the divisor here
IMO A
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05 Aug 2008, 17:57
spriya wrote:
rnemani 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

simple getting the number of multiples if 3 in 30 => 10 multiples here
hence 10 is the k which becomes the divisor here
IMO A

IMO C
Left out 3 in 6,9 etc
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Re: Factor question   [#permalink] 05 Aug 2008, 17:57
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