Why is the gcf of two even numbers are always even?

Answer 1

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.

Answer 2

Oh, dude, it's like this - when you're looking for the greatest common factor of two even numbers, they both have 2 as a factor, right? So, the greatest common factor will definitely have at least one 2 in it, making it even. It's just how the math cookie crumbles, man.

Answer 3

Well, isn't that a happy little question! When you find the Greatest Common Factor (GCF) of two even numbers, you're looking for the largest number that can evenly divide both of them. Since even numbers are always divisible by 2, the GCF of two even numbers will also be divisible by 2, making it an even number as well. It's just a lovely little pattern in the world of numbers!

Answer 4

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.

Answer 5

it is becuase it is always even