Q: Is the GCF of any two even numbers is always even?

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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.

That is correct.

True.

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.

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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.

That is correct.

No

Yes.

The GCF of any set of odd numbers is odd because odd numbers don't have any even factors.

True.

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.

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

Yes, that is true.

The GCF of an odd and even number is never even.

No, the GCF of any two numbers may be odd or even. For instance:The GCF of 2 and 4 is 2The GCF of 3 and 6 is 3The GCF of 14 and 21 is 7.