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# If n is a positive integer and n^2 is divisible by 72, then

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Intern
Joined: 12 Jan 2005
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If n is a positive integer and n^2 is divisible by 72, then [#permalink]  07 Oct 2005, 02:51
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is

a) 6
b) 12
c) 24
d) 36
e) 48
SVP
Joined: 24 Sep 2005
Posts: 1898
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Manager
Joined: 03 Aug 2005
Posts: 134
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I pick b.

72=3^2*2^3

n is at least 3*2^2
Director
Joined: 21 Aug 2005
Posts: 795
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n^2 is divisible by 72:
So,
n^2 = 72, n is not an integer
n^2 = 144, n = 12
...
n^2 = 576, n = 24
...
n^2 = (72)(72), n = 72

This implies that all perfect squares of n are multiples of 12. So 12 it is.
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