The prime factors of 30 are 2, 3 and 5. In addition to being the factors of 30, the numbers 2, 3 and 5 are also prime numbers, which means that they can only be divided evenly by either the number 1 or by themselves. The numbers 2, 3 and 5 are also the first three prime numbers.
Although finding the prime factors of a positive integer can be a multi-step procedure in some cases, determining the prime factors of the positive composite integer 30 can be easily accomplished by following two of the basic rules of factorization. The first of those rules states that an even number, such as 30 in this case, will always have 2 as one of its prime factors. Since that provides 2 as a factor, 30 divided by 2 equals 15. Another basic rule of factorization states that any number ending in 5 will have 5 as one of its prime factors. Since 15 is not a prime number, further division is required, which leads to 15 being divided by 5 equals 3. Because 3 is a prime number, no further division is necessary and the prime factorization of 30 is represented by 2 x 3 x 5 = 30.
The process of determining the prime factors of a positive integer is referred to as integer factorization. According to the fundamental theorem of arithmetic, each positive integer will possess its own single and unique prime factorization.