Factors are the numbers multiplied to get another number. For instance, 6 is factored as 2×3. Often, there is more than one way to factor a number; 12 can be factored as 2×6, 4×3, or 2×2×3. The last of these is composed of only prime numbers; it is the prime factorization of 12. A prime factorization includes every copy of every prime factor. Another example, the prime factorization of 8 is 2×2×2 or 23.
Prime numbers are a subset of the natural numbers N+. Prime numbers are those that are evenly divisible by themselves and by the number 1. The first few prime numbers are:
2, 3, 5, 7, 11, ...All other natural numbers, except 1, are called composite numbers. These can be expressed as factors of prime numbers. Here are the first few natural numbers expressed as prime or composite numbers:
1, 2, 3, 2×2, 5, 2×3, 7, 2×2×2, 3×3, 2×5, 11, ...Dividing by the smallest prime number that divides it and repeating this for each resulting quotient until a prime number is obtained can find the prime factorization of a composite number. For example, factor the composite number 24:
The prime factorization of 24 is 2×2×2×3, which may also be written 23×3.24 ÷ 2 = 12 12 ÷ 2 = 6 6 ÷ 2 = 3