If The GCD of two numbers (not equal, both integers, greater than 1) is 2, then which of the following can be true?
A. They are prime.
B. They are even.
C. They do not have a common prime factor.
D. They do not have a common factor other than 2.  Choices
A) Only A
B) Only B
C) Only C
D) Only D
E) Only B and D
The GCD of two numbers (not equal, both integers, greater than 1) is 2 means that they don't share factors other than 1 and 2.   This also means that both numbers are even ( divisible by 2.)   A. They are not prime. 2 is the only even number that is prime, so one number can be prime but the other number cannot be.   B. They are even. Since they are divisible by 2, they are even..   C. They have a common prime factor. The question defines the numbers as having a GCD of 2, which is prime.   D. They have a common factor other than 2. Both numbers have common factors of 2 and 1. For example:   The factors of 4 are 1 and 2, the factors of 6 are 1, 2, and 3.   Therefore, (Only B) is the only correct answer.
<result>B</result>
If The GCD of two numbers (not equal, both integers, greater than 1) is 2, then which of the following can be true?
A. They are prime.
B. They are even.
C. They do not have a common prime factor.
D. They do not have a common factor other than 2.