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What is the greatest common divisor of two different

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Manager
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What is the greatest common divisor of two different [#permalink] New post 15 Mar 2008, 00:19
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What is the greatest common divisor of two different positive integers which are less 144?

Please advise the best approach to this problem.
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: PS (GCD) [#permalink] New post 15 Mar 2008, 00:30
Expert's post
:? 71 (142 and 71)
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Re: PS (GCD) [#permalink] New post 15 Mar 2008, 02:30
walker, I know the answer. What is more interesting for me is approach.
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Re: PS (GCD) [#permalink] New post 15 Mar 2008, 04:15
Expert's post
This is my logic:

1. we have two different integers.
2. the largest GCD(x,y) of two integers when GCD(x,y)=x
3. if we choose one integer (x), the most closest different integer to give GCD=x is y=2x
4. apply for our problem: the largest integer in the set is 143 but 143 is odd. Therefore, we choose next one - 142 and 142/2=71.
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Re: PS (GCD) [#permalink] New post 15 Mar 2008, 04:52
Thanks for clear explanation!
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Re: PS (GCD) [#permalink] New post 15 Mar 2008, 17:20
az780 wrote:
What is the greatest common divisor of two different positive integers which are less 144?

Please advise the best approach to this problem.


The answer is 71.
71 is a divisor for 71 and for 142.
rkassal
Re: PS (GCD)   [#permalink] 15 Mar 2008, 17:20
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