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

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Director
Joined: 17 Oct 2005
Posts: 928
if n is a positive integer and n^2 is divisible by 72, then [#permalink]

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15 Dec 2005, 07:24
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if n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is what?
Director
Joined: 09 Jul 2005
Posts: 591

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15 Dec 2005, 11:19
automan wrote:
We don't know.

Upsss, I didn't consider the "must". I should have read more carefully.

n^2=K*72= K * 2 * 6 * 6

n= sqrt(2K)*6

Since n is an integer then sqrt(2K) must be un integer. The lowest integer that we can form varying K is sqrt(2K)=2. Therefore 12 must divide n.
15 Dec 2005, 11:19
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