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M is a positive integer, What is the greatest common factor

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Source: — Data Sufficiency |
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by Eggshells » Mon Jan 06, 2020 3:30 pm
BTGmoderatorLU wrote:Source: Manhattan Prep

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.

The OA is D
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
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