I would consider both prime and composite factors - depending on what was required.
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Only 1 goes into both of them evenly. You can use -1 if you have to, but we don't generally consider negative numbers as factors.
All nonzero numbers have factors. Some numbers have some of the same factors as other numbers. These are known as common factors. 3 is a common factor of 9 and 12.
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Yes. 1 and the number itself are factors of all numbers.
Prime numbers are 3 and 2. Factors are 1,2,3,6.