No. The square of an odd number will be odd and the square of an even number will be even.
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Half of all square numbers are odd. They are the ones which are the square of an odd number.
No, but only in the case of the number 1 (12=1) are square numbers odd.
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 square of any odd number is also an odd number for reasons that should be obvious.
Square numbers have an odd number of factors.