Data Sufficiency (DS) | If n is a positive integer, what is the greatest common factor

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