Why is the gcf of any even number always even?

Answer 1

By definition, every even number has 2 as a factor. That means that every set of even numbers will have at least 2 as a common factor. The GCF might be higher, but if it has 2 as a factor, it's even.

Answer 2

By definition, every even number has 2 as a factor. That means that, at a minimum, every set of even numbers will have a common factor of 2. The GCF could be higher, of course, but that common factor of 2 will always be there, making the numbers even.