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If n is a positive integer, what is the greatest common factor

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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.
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New post 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.
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Re: If n is a positive integer, what is the greatest common factor  [#permalink]

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New post 22 Sep 2018, 12:03
Hi Bunuel
I often struggle with such questions. What topic should I revisit to get better on such questions?
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New post 23 Sep 2018, 02:39
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hargun3045 wrote:
Hi Bunuel
I often struggle with such questions. What topic should I revisit to get better on such questions?


2. Properties of Integers




5. Divisibility/Multiples/Factors



For other subjects:
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If n is a positive integer, what is the greatest common factor  [#permalink]

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New post 23 Sep 2018, 12:12
Bunuel wrote:
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.


Hi Bunuel what if the n is in the form of 2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient.
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Re: If n is a positive integer, what is the greatest common factor  [#permalink]

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New post 23 Sep 2018, 20:47
LoneSurvivor wrote:
Bunuel wrote:
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.


Hi Bunuel what if the n is in the form of 2^p where none of the two factors of 2^p will add to a prime number. but we do not know what is the value of P so we certainly can not determine GCF .So statement 1 is not sufficient.


2^p is 2, 4, 8, ... For any of these values you can pick 1 and 2 as factors, which gives the sum of 3, which is a prime.
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Re: If n is a positive integer, what is the greatest common factor  [#permalink]

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New post 24 Sep 2018, 05:11
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Dear Bunuel,

Can you elaborate more about the line

(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.
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Re: If n is a positive integer, what is the greatest common factor  [#permalink]

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New post 24 Sep 2018, 05:16
vipulshahi wrote:
Dear Bunuel,

Can you elaborate more about the line

(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.


Any even number has at least the following factors: 1 and 2. The sum = 3 = prime.

(1) says that "No two different factors of n sum to a prime number". So, n is NOT even.
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Re: If n is a positive integer, what is the greatest common factor   [#permalink] 24 Sep 2018, 05:16
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