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

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

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11 Nov 2005, 04:22
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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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VP
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11 Nov 2005, 04:51
C)...how many 3s are in 30!...30/3+30/3^2+30/3^3=14
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SVP
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11 Nov 2005, 12:58
christoph wrote:
C)...how many 3s are in 30!...30/3+30/3^2+30/3^3=14

Christoph you are too good.

OA is indeed 14. (C)
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Intern
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14 Nov 2005, 22:59
For those of you who are still confused by this problem this is how to break it down:

multiply 1-30:
1 x 2 x 3 x 4 x 5 x (2x3) x 7 x 8 x (3x3) x 10 x 11 x (3x4) x 13 x 14 x (3x5) x 16 x 17 x (3x3x2) x 19 x 20 x (3x7) x 22 x 23 x (3x8) x 25 x 26 x (3x9) x 28 x 29 x (3x10)

There are 14 3s in there, therefore 3^14
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15 Nov 2005, 10:01
yup its C

14

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

total 14
15 Nov 2005, 10:01
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