A question for discussion on factors

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When does a factor have to be positive or even a whole number. And when does 1 count?

The factors of 18 are 1,2,3,6,9 and 18. What about the negatives of these?

If I am asked to factorise $${\frac{{\mathtt{x}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{y}}}{{\mathtt{3}}}}$$ then the answer would be $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)$$ so the fraction is classed as a factor.

By this logic $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$ is also a factor of 2 because $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{6}} = {\mathtt{2}}$$

That is, 1/3 goes into 2 an integer 'whole' number of times.

Melody Dec 18, 2014