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# If a and b are positive integers, what is the greatest common factor

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
If a and b are positive integers, what is the greatest common factor  [#permalink]

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22 Dec 2016, 01:30
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45% (medium)

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67% (01:22) correct 33% (01:40) wrong based on 93 sessions

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If a and b are positive integers, what is the greatest common factor of a and b?

(1) The greatest common factor of half of a and half of b is 7.
(2) a is 14 and b is an even multiple of 21

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Re: If a and b are positive integers, what is the greatest common factor  [#permalink]

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22 Dec 2016, 04:53
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1
(1) The greatest common factor of half of a and half of b is 7.

a/2 = 7x, b/2 = 7y

a = 14x, b = 14y

GCF (a, b) = GCF (14x, 14y) = 14 Sufficient.

(2) a is 14 and b is an even multiple of 21

a = 14, b = 21*2x, x > 0 -----> b > 0

b = 21*2, 21*4, 21*6, 21*8 ... = 3*7*2, 3*7*2^2, 3^2*7*2, 3*7*2^3 ...

If we take any value of b the GCF (a, b) = a = 14. Sufficient

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Re: If a and b are positive integers, what is the greatest common factor  [#permalink]

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18 Apr 2018, 11:52
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Re: If a and b are positive integers, what is the greatest common factor &nbs [#permalink] 18 Apr 2018, 11:52
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# If a and b are positive integers, what is the greatest common factor

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