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.

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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.