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Assuming the second even number is equal to 4 or greater, than the highest common factor of the two numbers is equal to an even number 2 or greater.

Why can't an odd factor be used? Any odd factor must be multiplied by (at least) 2 to create an even product (ie. the 1st even number). That same odd factor must be multiplied by (at least 2) and any other number to create a 2nd even product, thereby making the Greatest Common Factor (at least) 2 times the odd number....which is an even number.

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Q: Is the greatest common factor of two even numbers always even?
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