Final answer:
The greatest common factor of 6 and 12 is even.
Step-by-step explanation:
The student is asking whether the greatest common factor (GF) of 6 and 12 will be odd or even, without actually calculating it. To determine this, we need to look at the prime factors of both numbers. The prime factorization of 6 is 2 x 3, and the prime factorization of 12 is 2 x 2 x 3.
The GF is found by taking the product of the common prime factors. In this case, the only common prime factor is 2. So, the GF of 6 and 12 is 2. Since 2 is an even number, the GF of 6 and 12 is also even.