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Q: What is a reason why the GCF of any two even numbers is always even?

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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.

The GCF of two even numbers is always even.

Yes and yes.

A set of even numbers, yes.

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.

No

No. For example, the GCF of 8 and 12 is 4. The GCF of 12 and 18 is 6. The Greatest Common Factor of two even numbers will always be even, but it will not always be 2.

Yes.

Yes.

It is not always even. * * * * * Yes. Since the numbers are even, 2 must be a common factor and so the GCF is a multiple of 2.

No not always as for example the GCF of 7 and 21 is 7

That is correct.

Yes.

Yes.

No. The GCF of 4 and 8 is 4.

No. The GCF of 8 and 12 is 4.

Not always. The GCF of 8 and 12 is 4.

No, always odd.

True.

Yes.

Yes.

True.

no, the GCF for 4 and 2 would be 2, which is even

The GCF is, yes.

All even numbers have two as a factor. Any two even numbers have (at the least) two as a common factor. That means the GCF of any two even numbers will have two as a factor. Any number that has two as a factor is even.