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
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Number Properties
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xcusemeplz2009
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imo d
oa pls
oa pls
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vivek.kapoor83
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taking n = 12, n^2 = 144 which is divisible by 72
so, 12 is the largest no. thru which n divides.another eg doesnt satisfy
IMO B
so, 12 is the largest no. thru which n divides.another eg doesnt satisfy
IMO B
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grockit_jake
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Note you are not looking for n. You are looking for the largest positive integer that must divide n.
The smallest n = 12, so n^2 = 144, like you said. 144 is divisible by every answer choice. Since (e) is the greatest....
Note that 12 = 2*2*3, so 12^2 = 2*2*2*2*3*3.
72 = 6*6*2 = 3*3*2*2*2. You MUST have one more factor of 2 in order to get a perfect square (two 3s and four 2s).
The smallest n = 12, so n^2 = 144, like you said. 144 is divisible by every answer choice. Since (e) is the greatest....
Note that 12 = 2*2*3, so 12^2 = 2*2*2*2*3*3.
72 = 6*6*2 = 3*3*2*2*2. You MUST have one more factor of 2 in order to get a perfect square (two 3s and four 2s).
