Yes, that is correct.
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polyphony
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 difference between any numbers is always positive.
A positive number times a positive number is always positive. A negative number times a negative number is always positive. Therefore, any square number will be positive. Any number to the fourth power (a square times a square) will always be positive. And so on.
Yes.