Reduce to factors. Often used to solve polynomial equations with nice roots. ('Nice' may not be the correct mathematical term, but it will suffice.
Examples:
x^2 - 3x + 2 = (x-1)*(x-2)
6 = 2 * 3
This can be a help solving equations if, for example, we know that
x^2 - 3x + 2 = 0
then we know that
(x-1)*(x-2) = 0
If two numbers are multiplied to get zero, then one or both of them must be zero. This tells us that
(x-1) = 0
or
(x-2) = 0
If
x - 1 = 0
then
x = 1
Similarly
x - 2 = 0
x = 2
These are the solutions of the equation.
When factorising expressions without variables, the objective is normally to reach a list of prime factors. This is the most effective means of finding the lowest common multiple of a number. For example
18 = 3 * 3 * 2
12 = 3 * 2 * 2
3 * 3 * 2 * 2 = 36
This last expression contains just enough prime factors to make up each of the other numbers, so this number is the lowest number of which the other numbers are both factors.