Best Answer

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.

Q: Is the GCF of any two numbers always odd and why?

Write your answer...

Submit

Still have questions?

Continue Learning about Basic Math

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 false.

Yes.Yes.2 can never be a factor of an odd number and because of that it can't be a common factor of any number pair where at least one of numbers is odd.

Two even numbers won't have an odd GCF.

In the same way that and odd plus and even is always odd. For example, 7*3 = (7+7) odd + odd = even , then add +7, apply rule that odd + even = odd and get that it equals 21.

Related questions

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.

Any set of odd numbers, yes.

The GCF will, yes.

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

Yes and yes.

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

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.