 Factorization is not usually considered meaningful within number systems possessing division, such as the real or complex numbers, since any formula_1 can be trivially written as formula_2 whenever formula_3 is not zero.However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator.Factorization was first considered by ancient Greek mathematicians in the case of integers.