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# M is a positive integer, what is the greatest common factor of M and 6

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Manager
Joined: 01 Sep 2016
Posts: 201
GMAT 1: 690 Q49 V35
M is a positive integer, what is the greatest common factor of M and 6  [#permalink]

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Updated on: 20 Sep 2017, 01:35
6
00:00

Difficulty:

85% (hard)

Question Stats:

48% (01:34) correct 52% (02:03) wrong based on 58 sessions

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M is a positive integer, what is the greatest common factor of M and 64?

(1) No two different factors of M sum to a prime number.

(2) The greatest common factor of M and 2,310 is 165.

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we shall fight in the fields and in the streets,
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we shall never surrender!

Originally posted by bkpolymers1617 on 20 Sep 2017, 01:13.
Last edited by Bunuel on 20 Sep 2017, 01:35, edited 1 time in total.
Renamed the topic and edited the question.
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M is a positive integer, what is the greatest common factor of M and 6  [#permalink]

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20 Sep 2017, 06:07
1
bkpolymers1617 wrote:
M is a positive integer, what is the greatest common factor of M and 64?

(1) No two different factors of M sum to a prime number.

(2) The greatest common factor of M and 2,310 is 165.

Statement 1: every no has 1 as a factor. as per this statement M does not contain 2 because in that case 1+2=3=prime number and its given summations of no two different factors of M are prime. So it can be concluded that M is odd. Hence Greatest common factor of M & 64 will be 1. Sufficient

Statement 2: 2310=2*3*5*7*11 and 165 = 3*5*11. As 165 is GCF of M & 2310, it is evident that M does not contain 2, so M has to be odd.
Hence GCF of M & 64 is 1. Sufficient

Option D
Manager
Joined: 01 Sep 2016
Posts: 201
GMAT 1: 690 Q49 V35
Re: M is a positive integer, what is the greatest common factor of M and 6  [#permalink]

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20 Sep 2017, 06:51
That is perfect my friend. Correct answer and solution:)

Posted from my mobile device
_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Re: M is a positive integer, what is the greatest common factor of M and 6 &nbs [#permalink] 20 Sep 2017, 06:51
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