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# If n is the product of the integers from1 to 20 inclusive,

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Intern
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If n is the product of the integers from1 to 20 inclusive, [#permalink]  11 Dec 2008, 13:07
If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?

A. 10
B. 12
C. 15
D. 18
E. 20
Manager
Joined: 15 Oct 2008
Posts: 110
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Re: product [#permalink]  11 Dec 2008, 13:26
D. k=18

Take all the even numbers from 1 to 20 inclusive: 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.
2 = 2*1
4=2*2
6=2*3
8=2*2*2
10=2*5
12=2*2*3
14=2*7
16=2*2*2*2
18=2*3*3
20=2*2*5
There is a total of 18 factors 2 in the product of n.
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Location: New York
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Re: product [#permalink]  13 Dec 2008, 20:04
1
KUDOS
gorden wrote:
If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?

A. 10
B. 12
C. 15
D. 18
E. 20

=20/2^1 (nearest integer floor) + 20/2^2 (nearest integer floor) + 20/(2^3) (nearest integer floor)+20/(2^4)(nearest integer floor)
= 10+5+ 2+1
=18
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Senior Manager
Joined: 30 Nov 2008
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Schools: Fuqua
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Re: product [#permalink]  13 Dec 2008, 21:54
x2suresh wrote:
gorden wrote:
If n is the product of the integers from1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?

A. 10
B. 12
C. 15
D. 18
E. 20

=20/2^1 (nearest integer floor) + 20/2^2 (nearest integer floor) + 20/(2^3) (nearest integer floor)+20/(2^4)(nearest integer floor)
= 10+5+ 2+1
=18

x2suresh,

can you please explain how you came up with the figures. Is it some sort of formula?
Re: product   [#permalink] 13 Dec 2008, 21:54
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