## What is a prime number?

If you remember, a prime number is any whole number that is greater than 1 that only has 2 factors. Those factors are 1 and itself. Factors are just the numbers that are multiplied together to equal a given number.

## What is a composite number?

A composite number is any number greater than one that has multiple factors. For example, the number 6 has 4 factors, (1,2,3,6) because 1 times 6 is 6 and 2 times 3 is 6.

Composite numbers are called composite for a reason. It is because they are composed of prime numbers.

Let’s look at all of the prime numbers out there less than 20.

They are: 2, 3, 5, 7, 11, 13,17 and 19.

But let’s look at a composite number less than 20 and see the factors.

Take the number 9. The factors of 9 are 1, 3, and 9. But if you look at the prime numbers that make up 9, you can see that the prime factors of 9 will be 3 times 3.

Look at the number 4. The factors of 4 can be broken down into prime numbers of 2 times 2 as 2 is a prime number.

## What is prime factorization?

The process of breaking down composite numbers into their prime factors is called prime factorization.

Let’s go over the prime factorization process using something they call a “factor tree”.

Let’s find the prime factors of the number 18.

The first step is to identify 2 factors that multiply together to equal 10.

Let’s take 2 times 9.

Using 2 and 9 as our factors, we can use the factor tree to write down 2 x 9 as the first level in our tree. 2 is a prime number but 9 is still a composite.

What prime numbers are factors of 9? The answer is 3.

Our last branch of our tree is made up of all prime numbers so we know that we are done.

So you would write the prime factorization of 18 as 2 x 3 x 3.

Let’s look at the same number of 18 but start off with 2 different factors. Let’s use the factors 3 x 6.

Well, 3 is a prime number but 6 is not. What prime numbers can be multiplied together to equal 6? The answer would be 2 x 3.

Adding our next branch to our tree you see that we have gotten all the way to all prime numbers so we write the prime factorization of 18 as being 2 x 3 x 3. It is the same answer we received when starting with the factors of 2 x 9.

Be sure to check out my YouTube video above to see more examples. If you would like to download a free printable worksheet on prime factorization, you can use the links below. There is a worksheet and answer sheet.

For more practice problems on math concepts, check out my additional resources page here.