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01 Aug 2018, 20:50
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If n is a positive integer, what is the greatest common factor of n and 64?
(1) No two different factors of n sum to a prime number.
(2) The greatest common factor of n and 2,310 is 165.
(1) No two different factors of n sum to a prime number.
(2) The greatest common factor of n and 2,310 is 165.
01 Aug 2018, 20:59
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If n is a positive integer, what is the greatest common factor of n and 64?
Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).
(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
Answer: D.
Hope it's clear.
Notice that 64 = 2^6. So, the GCF of n and 2^6 is either 1 or some power of 2 (from 2 to 2^6).
(1) No two different factors of n sum to a prime number. This implies that 2 is NOT a factor of n, if it were then the sum of two factors of n, 1 and 2, would be a prime number. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
(2) The greatest common factor of n and 2,310 is 165. So, the GCF of n and some even number is NOT even. This implies that 2 is NOT a factor of n. Since 2 is not a factor of n, then the GCF of n and 2^6 is 1. Sufficient.
Answer: D.
Hope it's clear.
23 Sep 2018, 02:39
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