Number of Factors of 6

Question

1. factor of 6 is 1,2,3,6, or
2. factor of 6 is 1,2,3,6,-1,-2,-3,-6

Which one is correct?

Answer 1

We generally only consider positive factors, so the correct answer is (1).

Answer 2

Which is correct depends on the context. If you are working with positive integers, the first answer would be correct. If you are working with integers the second is correct. If you are working with rational numbers neither is correct.

Quite often we look at the prime factorisation of some expression and say that it is unique up to multiplication by units. The units in the integers are $\pm 1$, hence the two points of view. Every non-zero rational is a unit, because the rationals form a field.