The prime factorization of 30 is 2 * 3 * 5

Start with the lowest prime number that will divide into the given number evenly.

The result will be one of the prime factors and a number that might need to be factored. In the case of 30, 2 is a prime number and 15 needs to be factored further.

The lowest number that will divide into 15 evenly is 3. 3 * 5 equals 15. 5 is also a prime number, so the prime factorization of 30 is 2 * 3 * 5.

To find the prime factors of any number then divide the number by prime numbers of increasing value. When a prime number wholly divides the original number repeat the process with the same prime number but each time with the new quotient until complete division does not occur. Repeat with a prime number of higher value until the final quotient is 1.

30 ÷ 2 = 15

15 ÷ 2 complete division does not occur

15 ÷ 3 = 5

5 ÷ 3 complete division does not occur

5 ÷ 5 = 1 : quotient = 1, prime factorization is complete

The prime factors are therefore 2, 3 and 5.

2 x 3 x 5 = 30