In mathematics, to factor a number or algebraic ex- pression is to find parts whose product is the original number or expression. For instance, 12 can be factored into the product 6 􏰀 2, or 3 􏰀 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 num- ber is a number whose only factors are itself and 1 (the first few prime numbers are 1, 2, 3, 5, 7, 11, 13). Inte- gers that are not prime are called composite. The num- ber 99 is composite because it can be factored into the product 9 􏰀 11. It can be factored further by noting that 9 is the product 3 􏰀 3. Thus, 99 can be factored into the product 3 􏰀 3 􏰀 11, all of which are prime. By saying “in essentially one way,” it is meant that although the factorsof99couldbearrangedinto3􏰀11􏰀3or11􏰀 3 􏰀 3, there is no factoring of 99 that includes any primes other than 3 used twice and 11.