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

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Math Forum Moderator
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What is the greatest common divisor of two positive integers a and b? [#permalink]

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21 Dec 2009, 12:05
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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

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Last edited by Bunuel on 20 Jan 2015, 12:59, edited 2 times in total.
Renamed the topic, edited the question and added the OA.

Kudos [?]: 5486 [0], given: 112

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What is the greatest common divisor of two positive integers a and b? [#permalink]

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21 Dec 2009, 12:16
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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.

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Re: What is the greatest common divisor of two positive integers a and b? [#permalink]

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21 Dec 2009, 13:13
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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Math Forum Moderator
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Re: What is the greatest common divisor of two positive integers a and b? [#permalink]

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21 Dec 2009, 13:18
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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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: What is the greatest common divisor of two positive integers a and b? [#permalink]

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20 Jan 2015, 12:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the greatest common divisor of two positive integers a and b? [#permalink]

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20 Jan 2015, 13:00
Similar question to practice: what-is-the-greatest-common-divisor-of-distinct-positive-102181.html
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Re: What is the greatest common divisor of two positive integers a and b? [#permalink]

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18 Jul 2016, 05:32
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the greatest common divisor of two positive integers a and b?   [#permalink] 18 Jul 2016, 05:32
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