Question

Why is the GCF of any two even numbers is always even?

Answer 1

Suppose A and B are two even numbers. Then, by definition,
A = 2*P for some integer P, and
B = 2*Q for some integer Q
So 2 is a factor of both A and B, that is it is a common factor. 

Now, any common factor of A and B is, by definition, a factor of their HCF. That is, 2 is a factor of the HCF of A and B: in other words, the HCF is even.

All even numbers have two as a factor. That means that any set of even numbers will have at least a two as a common factor. Since 2 will be a part of the greatest common factor, it will have to be even.
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Answer 2

Answer:

The GCF of any two even number is always even

Step-by-step explanation:

Given that GCF (Greatest common factor) of a any two even numbers is always even

   2 an even number is the first factor of any even number which means in a set of two even numbers each number will have 2 as common factor and it will be the part of the greatest common factor therefore the GCF of any two even numbers is always even