Question

1. use a counterexample determine whether each statement is true or false. if true, explain why. if false, give a counterexample. a. the gcf of any two even numbers is always even.

Explanation:

All even numbers are divisible by 2, so 2 is a common factor of any two even numbers. The greatest common factor (GCF) must include this common factor of 2, meaning the GCF itself is divisible by 2 and thus even. There is no counterexample because the statement holds for all pairs of even numbers.

Answer:

True. All even numbers have 2 as a common factor, so their GCF will always be a multiple of 2 (even).