jmc

The positive factors of $12$ are $1,2,3,4,6,$ and $12$. The negative factors of $12$ are $-1,-2,-3,-4,-6,$ and $-12$. When we add these twelve numbers together, we can pair each positive factor with its negation: $$\begin{array}{rl}[1+(-1)]+[2+(-2)]+[3+(-3)]& +[4+(-4)]\\ +[6+(-6)]+[12+(-12)]& =0+0+0+0+0+0\\ & =\boxed{0}.\end{array}$$