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# If N is an integer ,and N^2 is divisible by 72, what is the

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CEO
Joined: 15 Aug 2003
Posts: 3469
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If N is an integer ,and N^2 is divisible by 72, what is the [#permalink]  22 Aug 2003, 21:46
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If N is an integer ,and N^2 is divisible by 72, what is the largest integer that MUST divide N is ?

1.6
2.12
3.24
4.36
5.48

Thanks
Praetorian
CEO
Joined: 15 Aug 2003
Posts: 3469
Followers: 61

Kudos [?]: 701 [0], given: 781

Re: PS - Divisibility ...Need Akamai for this one [#permalink]  22 Aug 2003, 21:59
AkamaiBrah wrote:
praetorian123 wrote:
If N is an integer ,and N^2 is divisible by 72, what is the largest integer that MUST divide N is ?

1.6
2.12
3.24
4.36
5.48

Thanks
Praetorian

Yes, the answer is 12, i would be very grateful if you can explain.
Manager
Joined: 14 Aug 2003
Posts: 88
Location: barcelona
Followers: 1

Kudos [?]: 0 [0], given: 0

72=(2^2)*(3^2)*2
N^2=x*72=x*(2^2)*(3^2)*2, x integer... N integer, so x=2*y^2, y integer... N=2*3*2*y, y integer... the largest number that MUST divide N is 2*3*2=12
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
Followers: 5

Kudos [?]: 41 [0], given: 0

i think it should be smallest integer.
because if N divisible by 48 and N is atleast 48 and 48 * 48 is divisible by 72
Whereas if N is divisible by 6 and N=6 then N^2 is not divisible by 72.
so 12 is the least divisor of N
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