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

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

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07 Sep 2016, 10:19
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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 o [#permalink]

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07 Sep 2016, 10:49
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duahsolo wrote:
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

(1) The greatest common factor of half of a and half of b is 7. ==> a = 2*7 *something and b =2*7*something else

or, HCF (a,b) =14. -- Sufficient.

(2) a is 14 and b is an even multiple of 21 ==> b is even multiple of 21 means b has both 2 and 7 in it. Hence, HCF = 14. -- Sufficient.

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

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05 Oct 2017, 20:29
(1) The greatest common factor of half of a and half of b is 7. ==> x = 2*7 *something and y =2*7*k
HCF (a,b) =14. -- Sufficient.

(2) a is 14 and b is an even multiple of 21 ==> b is even multiple of 21 means b has both 2 and 7 in it. Sufficient.

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Re: If a and b are positive integers, what is the greatest common factor o   [#permalink] 05 Oct 2017, 20:29
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