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# What is the greatest common divisor of integers r and s ?

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Re: What is the greatest common divisor of integers r and s ? [#permalink]
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bm2201 wrote:
Statement 1: The greatest common divisor of 2r and 2s is 10.
Given 2 integers r, s
greatest divisor of 2r, 2s = 10 => greatest divisor of r, s = 5. (for any combination of r, s).

So Sufficient.

Bunuel chetan2u

Is this a property of GCD ?

Yes that would be true always if r and s are integers.
Basically you have 10 as GCD of 2r and 2s, which will be same as 2*(GCD of r and s)
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Re: What is the greatest common divisor of integers r and s ? [#permalink]
Bunuel wrote:
What is the greatest common divisor of integers r and s ?

(1) The greatest common divisor of 2r and 2s is 10.
(2) r and s are both odd.

DS21281

(1) If the greatest common divisor of 2r and 2s is 10, the greatest common divisor of r and s is 5. SUFFICIENT.

(2) If r and s are both odd, we can get multiple values.

if r = 3 and s = 9, the greatest divisor is 3. If r = 5 and s = 25, the greatest divisor is 5. INSUFFICIENT.

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Re: What is the greatest common divisor of integers r and s ? [#permalink]
GMATNinja, can you please advice whether it is possible for r to contain additional 2, but s should not contain 2? GCD is the common factor raised to the lowest power. So, if r contains additional 2--> 2r=2^2r , but s does not contain additional 2, 1 is still lowest power for common factor 2.
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Re: What is the greatest common divisor of integers r and s ? [#permalink]
r = a × b
s = a × c
GCD (r, s) = a

2r = 2 × a × b
2s = 2 × a × c
GCD (2r, 2s) = 2a

No matter r and s have or don't have the number 2 as one of its factors respectively, 2r and 2s always include the number 2 as one of their common divisor.
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Re: What is the greatest common divisor of integers r and s ? [#permalink]
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Re: What is the greatest common divisor of integers r and s ? [#permalink]
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