All nonzero numbers have factors. Some factors are even numbers, some factors are odd numbers.
Every even number has odd and even factors.
A perfect square.
Odd
Not only can they, but they must. An odd number cannot have an even factor. So none of the factors of either of the two odd numbers can be even and so the GCF is made up of only odd factors and so it must be odd.
At least one of the factors of an even number must be even, because the product of odd factors is always odd.
No. Odd numbers only have odd factors. They could not have an even factor in common.
The GCF of an odd and even number is never even.
even
48 has both even and odd factors.
Some even numbers have more factors than some odd numbers and some odd numbers have more factors than some even numbers. As a group, even numbers have more factors than odd numbers.
Some even numbers have more factors than some odd numbers and some odd numbers have more factors than some even numbers. As a group, even numbers have more factors than odd numbers.
Even numbers must have 2 amongst their factors; they may have other even numbers amongst their factors. Odd numbers must not; every factor of an odd number must be odd.
The number of factors can be either even or odd.
Both odd and even numbers may have odd numbers as factors.
Not only can they, but they must. An odd number cannot have an even factor. So none of the factors of either of the two odd numbers can be even and so the GCF is made up of only odd factors and so it must be odd.
Odd.
Both. 9 has three factors. 11 has two factors.
An even power. Square numbers have an odd number of factors.
No. The opposite is true: the gcf of an odd number and an even number is always odd. All the factors of an odd number are odd; or to put it another way: If a number has an even factor, the number itself must be even. Thus the only common factors between odd and even numbers must be odd.
The GCF of an odd and an even number must be odd since odd numbers do not have any even factors.