How to Do Prime Factorization

By Contributor; Updated April 24, 2017
A calculator can help you find the prime factorization.

Prime factorization refers to expressing a number as the product of prime numbers. Prime numbers are numbers that only have two factors: 1 and itself. Prime factorization is not as hard as it may seem. This article discusses how to go about solving prime factorization problems.

Learn a short list of prime numbers. 2, 3, 5, 7, 11, 13, 17, and 19 are all prime. There are more prime numbers than those mentioned, of course.

Start solving a prime factorization problem by writing the given number as the product of any two integers and go from there.

If one or both of the integers you write down is not prime, write it as the product of two smaller integers.

Repeat step 3 until you have written the given number as the product of two or more prime numbers.

Verify your answer with a calculator.

As an example, let's write the prime factorization of 360. Well, 360 = 36_10. Since neither 36 nor 10 is a prime number, we are not done. 36 = 9_4 and 10 = 2_5. 2 and 5 are both prime, so we have part of the answer. Let's look at 9_4. Neither number is prime. 9 = 3_3 and 4 = 2_2. 3 and 2 are prime, so we have 360 = 2_5_3_3_2*2, which is the answer.

Tip

Don't be afraid to write things down. Prime factorization is difficult to do mentally.

Warning

If you struggle with multiplication, prime factorization is challenging.

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