If the GCD of two distinct numbers (not equal, both integers, greater than 1) is 3, then which of the following can be true?
A. They are prime.
B. They are not even.
C. They do not have a common prime factor.
D. They do not have a common factor other than 3.  Choose the correct choice from the following answers: A) Only A B) Only B C) Only C D) Only D E) Only A and D
The GCD of two distinct numbers (not equal, both integers, greater than 1) is 3 means that they don't share factors greater than 3. Allowed factors are 1, 2, and 3. Defined factors are 1 and 3. The sequence is (3, 6, 9, 27, 81,...).   A. They are not prime. 3 is the only prime number that is divisible by 3, so one number can be prime but the other number cannot be.   B. They cannot be even. For example: 6 is the only allowed even number in the sequence and has factors of 1, 2, and 3 (1 x 2 x 3), all other numbers divisible by 3 and 2 (to be even) are also divisible by 6.   C. They do have a common prime factor. That prime factor is 3.   D. They have a common factor other than 3. Both numbers have common factors of 3 and 1.   Therefore only (Only B) is correct.
<result>B</result>
If the GCD of two distinct numbers (not equal, both integers, greater than 1) is 3, then which of the following can be true?
A. They are prime.
B. They are not even.
C. They do not have a common prime factor.
D. They do not have a common factor other than 3.