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

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

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17 Nov 2005, 13:12
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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?
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17 Nov 2005, 13:19
Looks like i am missing something

largest positive integer that must divide n

isn't it n itself?

if that is the case, n can be any thing for example it can be multiple of 72.
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17 Nov 2005, 13:25
12...n can be 12 or 144, etc..12 divides 144 as well as 12 but 144 divides 144 but not 12. so 12 is the largest integer for the statement to be true...
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17 Nov 2005, 13:27
hmmm...I think 12 should be the answer

think of it this way

N^2=72m where m is some integer

lets break 72 to its primes...2.36 or 2^3*3^2

n^2=2^3.3^2; then n=2^2.3

so N should be divisible by 12....the largest integer...
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17 Nov 2005, 13:49
nakib77 wrote:
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is?

Agree with duttsit. This dude is always right

It is 'n'

We know n=12 satisfies this condition. So will 12*2 = 24, 36, 48 and so on.

Ex: n=24, n^2=576 (Also, 576/72 = 8)
...
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17 Nov 2005, 13:56
christoph wrote:
12...n can be 12 or 144, etc..12 divides 144 as well as 12 but 144 divides 144 but not 12. so 12 is the largest integer for the statement to be true...

Cris ... you are too good.

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17 Nov 2005, 14:02
nakib77 wrote:
christoph wrote:
12...n can be 12 or 144, etc..12 divides 144 as well as 12 but 144 divides 144 but not 12. so 12 is the largest integer for the statement to be true...

Cris ... you are too good.

nakib, isn't 24 larger than 12 and doesn't n=24 satisfy the conditions? What is the source and OE?
If you got the answer choices and 12 is the only one in them that is a multiple of 12, then ..
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17 Nov 2005, 14:09
gsr wrote:
nakib, isn't 24 larger than 12 and doesn't n=24 satisfy the conditions? What is the source and OE?

looks like question is asking the maximum positive integer that divide ANY n.

So for example,
if n = 12, n^2 = 144 which is divisible by 72

but 24 does not divide 12

i still believe question could have been more clear.
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17 Nov 2005, 14:17
duttsit wrote:
gsr wrote:
nakib, isn't 24 larger than 12 and doesn't n=24 satisfy the conditions? What is the source and OE?

looks like question is asking the maximum positive integer that divide ANY n.
So for example,
if n = 12, n^2 = 144 which is divisible by 72
but 24 does not divide 12
i still believe question could have been more clear.

True 24 does not divide 12.

"If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is"

n=24 is a +ve integer
n^2 = 576 and (n^2)/72 = 8 -> so divisible by 72
n=24 holds true for the conditions and the largest number that can divide 24 is 24.
That's why I think we just need the answer choices.
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17 Nov 2005, 21:17
12

n^2 is divisible by 72

so the number divisible by 72 and are square , 144 (12*12) , 24*24, 48*48

if you notice this pattren only 12 is the number which will divide all the possible values of n (24 48 96 ....) which satisfy the equation n^2 = m 72

any higher number will not divide the lower values like 24 can't divide 12 ...
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18 Nov 2005, 22:09
fresinha12 wrote:
hmmm...I think 12 should be the answer

think of it this way

N^2=72m where m is some integer

lets break 72 to its primes...2.36 or 2^3*3^2

n^2=2^3.3^2; then n=2^2.3

so N should be divisible by 12....the largest integer...

Fresinha12, I like your approach the best. ...
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19 Nov 2005, 00:19
I understand now! Kill me not Bill
19 Nov 2005, 00:19
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