Prime factorization

Share lesson:

Share this lesson:

Copy the link to this lesson

Copy link

Google Classroom

Facebook

Twitter

The prime factorization of a number is all of the

that multiply to make that number. You can write the prime factorization of a number as a multiplication sentence.

How can you find the prime factorization of a number?

Use a factor tree! Follow these steps to make a factor tree:

Let's try it with 18. Since

let's use 2 and 9 as the first factors.

Now look at 2 and 9. The number 2 is prime, so stop there. The number 9 is not, since

Write those numbers under 9.

The number 3 is prime. The tree is finished! You have all of your prime factors now.

To write the prime factorization of 18, write each of those prime factors in a multiplication sentence.

Tips

Do not use the number 1 as a factor in your factor tree. The number 1 is neither prime nor composite.
There is only one set of prime factors for each number. For example, there is no set of prime numbers other than
2
×
3
×
3
that can multiply to 18.
Prime factorizations are usually written with the factors ordered from smallest to largest. For example, the prime factorization of 42 would be written as
42
=
2
×
3
×
7
.