Q: Is the GCF of any set of odd numbers always odd?

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

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.

The GCF will, yes.

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

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

Yes and yes.

Yes.

The GCF of any two odd numbers is also odd.

No. The gcf of 98 and 100 is 2 .

The gcf of a single number is the number itself. But you will usually want to take the gcf of more than one number, not of a single number.

Because odd numbers don't have any even factors so they can't have any in common.