In mathematics, a factor is a number or algebraic expression that divides another number or expression evenly. Therefore, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. This is the factorization of 24, and is one of two ways to list its factors. The other method is prime factorization, and in this case, the prime factors of 24 are 2, 2, 2 and 3.
With standard factorization, each factor pairs with another to multiply together to get the factored number. For example, 2 pairs with 12 because 2 x 12 = 24. Furthermore, when 24 is divided by any of these numbers, there is no remainder, decimal or fraction. The quotient of a number divided by any of its factors is always a whole number, and it is also a factor of the number.
Prime factorization involves breaking down the pairs of factors of a number even further. Each number must be written as the product of two or more prime numbers. A prime number is divided evenly only by 1 or itself. For example, the pair 6 and 4 multiply to get 24, but neither is prime. Dividing both by 2, however, gives 6 = 2 x 3 and 4 = 2 x 2. This gives the prime factorization of 24. The prime factors are calculated using any pair of factors and are always the same.