Question

Is the greatest common factor of any two even numbers always even

Answer 1

yes, the gcf of even numbers would always be even because both of the numbers are divisible by 2 which makes 2 a factor of both the numbers, so the gcf should be even too.

Answer 2

yes becaus any even numbers can be represented as 2n where n is an integer

so 2n and 2m where m and n aer both integers
they both have 2 as a factor so that will be included in finding the greatest common factor