Question

The GCF of any two even numbers is always even. Determine whether the statement is true or false. If true, explain why. If false, give a reason.

Answer 1

It is true that the GCF of any two even numbers is always even. GCF refers to the greatest common factor that two or more numbers have, and obviously it is going to be an even number. Take 18, 30, and 42 as your example - their GCF will be 6, which is an even number, as are those three numbers. GCF of odd numbers will be odd, and GCF of an odd and even number is also always even.

Answer 2

The question is asking us whether it is true that The GCF of any two even numbers is always even. GDF means the greatest common factor, for example the GCF of 24 and 32 is 8 - it's the biggest of their factors. The GCF is a multiple of all the (prime) common factors, and 2 is a common factor of two even numbers, so GCF will always be even - this is true!