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What is the greatest common divisor of two positive integers a and b?

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What is the greatest common divisor of two positive integers a and b? [#permalink] New post 21 Dec 2009, 11:05
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What is the greatest common divisor of two positive integers a and b?

(1) a and b share exactly one common factor.
(2) a and b are both prime numbers.
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jan 2015, 11:59, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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What is the greatest common divisor of two positive integers a and b? [#permalink] New post 21 Dec 2009, 11:16
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What is the greatest common divisor of two positive integers a and b?

(1) a and b share exactly one common factor --> since 1 is the common factor for all integers, and since given that a and b share only one common factor, then the greatest common divisor of a and b must be 1. Sufficient.

(2) a and b are both prime numbers. Two different primes share only 1 as a common factors, but as a could be equal to b, greatest common factor could be a (b) in this case. Hence insufficient.

Answer: A.
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Re: What is the greatest common divisor of two positive integers a and b? [#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: What is the greatest common divisor of two positive integers a and b? [#permalink] New post 21 Dec 2009, 12:18
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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
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Re: What is the greatest common divisor of two positive integers a and b? [#permalink] New post 20 Jan 2015, 11:05
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Re: What is the greatest common divisor of two positive integers a and b? [#permalink] New post 20 Jan 2015, 12:00
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Re: What is the greatest common divisor of two positive integers a and b?   [#permalink] 20 Jan 2015, 12:00
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