To factor a number means decomposing it to numbers, which when multiplied, the original number is obtained. Usually the mathematical expression is given in the form of equations, polynomials. Factoring polynomials means the breaking of polynomials into simpler terms, factors. Also, when the simple factors multiply, the original polynomial is obtained. Factoring helps in solving complex equations, making it easier to work with them.
The greates common factor is the greatest factor that is common to all terms. Mathematical expression - the equation is fully factored, when further factoring is not possible. In this case, the factoring looks like this:
x² - 14x + 48 = (x - 8)(x - 6)