Yes and 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.
The greatest common factor (GCF) of two even numbers is always even because both numbers are divisible by 2. Since the GCF is the largest integer that divides both numbers without leaving a remainder, it must also be divisible by 2. Therefore, the GCF itself is even, as it shares this common factor of 2 with both original even numbers.
no, the GCF for 4 and 2 would be 2, which is even
The GCF of two even numbers is even.
If x is an odd number that is a common factor of 2 even numbers, so is 2x. So the answer is yes.
The GCF of two even numbers is always even.
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.
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. 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.
A set of even numbers, yes.
Yes.
No, their GCF is always odd.
Yes.
Yes.
That is correct.
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.
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.