Given the product of a multiplicative expression, factoring is the process of breaking a number down into its smaller factor components. For example, the integer $12$ can be factored in several different ways: Similarly, multiplicative algebraic expressions, such as $4x^3,$ can be rewritten by rewriting their coefficients and variables as a product of their factors. The prime factorization of a multiplicative expression occurs when all of its factors are prime. This is true for both prime numbers and prime polynomials.