A question to ponder on factors

A question for discussion on factors

.

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.