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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] New post 05 Aug 2008, 07:29
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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Re: Factor question [#permalink] New post 05 Aug 2008, 07:32
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 :-D
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Re: Factor question [#permalink] New post 05 Aug 2008, 07:35
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
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Re: Factor question [#permalink] New post 05 Aug 2008, 07:37
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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
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Re: Factor question [#permalink] New post 05 Aug 2008, 07:39
"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

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Re: Factor question [#permalink] New post 05 Aug 2008, 09:52
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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Re: Factor question [#permalink] New post 05 Aug 2008, 16:55
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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Re: Factor question [#permalink] New post 05 Aug 2008, 16:57
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, 16:57
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If p is the product of the integers from 1 to 30, inclusive,

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