Non-examples are infinite. One relevant one is a number that cannot be divided into a number.
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The greatest common factor of 6 and 9 is not 5.
A non-factor.
Any non-zero integer can be a common factor.
A factor is a number that divides evenly into another number with no remainder. 3 is a factor of 9. 4 is not a factor of 9.
1 is a non-rectangular number. The only factor of 1 is 1.