In mathematics, to factor a number or algebraic expression is to find parts whose product is the original number or expression. For instance, 12 can be factored into the product 6 x 2, or 3 x 4. The expression (x² - 4) can be factored into the product (x + 2)(x - 2). Factor is also the name given to the parts. We say that 2 and 6 are factors of 12, and (x-2) is a factor of (x² - 4). Thus we refer to the factors of a product and the product of factors.

The fundamental theorem of arithmetic states that every positive integer can be expressed as the product of prime factors in essentially a single way. A prime number is a number whose only factors are itself and 1 (the first few prime numbers are 1, 2, 3, 5, 7, 11, 13). Integers that are not prime are called composite. The number 99 is composite because it can be factored into the product 9 x 11. It can...