No not always as for example the GCF of 7 and 21 is 7
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The GCF of an odd and even number is never even.
The GCF of 2 and any even number is 2.
The GCF of any set of odd numbers is odd because odd numbers don't have any even factors.
By definition, every even number has 2 as a factor. That means that every set of even numbers will have at least 2 as a common factor. The GCF might be higher, but if it has 2 as a factor, it's even.
There's a lot of possibilities. Any set of consecutive even numbers has a GCF of 2.