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what is the greatest common divisor of two positive int a

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what is the greatest common divisor of two positive int a [#permalink] New post 21 Dec 2009, 11:05
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Q... what is the greatest common divisor of two positive int a and b?
I. a and b share exactly one common factor.
II. a and b are both prime numbers.
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Re: ds [#permalink] New post 21 Dec 2009, 11:16
Expert's post
chetan2u wrote:
Q... what is the greatest common divisor of two positive int a and b?
I. a and b share exactly one common factor.
II. a and b are both prime numbers.


(1) As 1 is the common factor for all integers, and given that a and b share only one common factor, hence it's 1. Sufficient.

(2) Two different primes share only 1 as common factors, but as a can be equal to b, greatest common factor would be a (b) in this case. Hence insufficient.

Answer: A.
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Re: ds [#permalink] New post 21 Dec 2009, 12:13
If both numbers are prime, don't we then know that 1 is the greatest common divisor by definition? Isn't II) saying the same thing as I)?
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Re: ds [#permalink] New post 21 Dec 2009, 12:18
we can not rule out the possibility of both a and b being the same prime no.... in that case the greatest divisor would be the prime no itself
Re: ds   [#permalink] 21 Dec 2009, 12:18
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