Q: Is it true the gcf of any two numbers always even and why?

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True.

Yes, that is true.

Yes.

It is false.

True. Even numbers are even because they are multiples of 2. That means that any two even numbers will have at least 2 as a common factor. Since that number (the GCF) will have 2 as a factor, it will be a multiple of 2: an even number.

The GCF of any two odd numbers is always odd. The GCF of any two even numbers is always even. The GCF of an odd and an even number is always odd.

By definition, an even number has 2 as a factor. That means that any set of even numbers will have at least a common factor of 2. Since that common factor will also have 2 as a factor, it has to be even.

No, it is not true: it depends on what your numbers are.

There are two truths about odd numbers. When added you get an even number... always! When multiplied you get an odd number... always!

YES. The product of any two consecutive numbers is even because their product is always a multiple of 2.Examples:2 * 3 = 63 * 4 = 12

The GCF of any two odd numbers is always odd because odd numbers don't have any even factors. The GCF of any two even numbers is always even because even numbers are divisible by two and any common factors would have at least one two in common. The GCF of an even and an odd number is odd because odd numbers don't have any even factors.

Yes.