Factors in algebra are used almost all the time outside school! Considering that factors tell you which numbers to multiply to give any given number; seemingly simple stuff like say deciding how many basketball teams one can create from a group of 35 at any one time requires one to use the fact that 5 & 7 are two factors that make 35. Infact, any problem solving that requires you to group, share out, divide and even rearrange patterns/shapes will involve knowing the factors that make up numbers. The biggest advantage (in my opinion) is that every number can be written as a multiplication of its factors... This way we have the ability split up any number and thus work out who gets how much of whatever!
If your talking about factors in algebra I never used those outside of school but I'm sure if you become a mathematician you may use them. They are probably also useful in physics. You can use them to find the roots of a function so you know when y will have a value of 0. It could help you to draw a parabola opening upward or downward.