# What is Prime Factorization?

A prime number is any number that can only be divided by either one or by itself.

Which means that a prime number will always be odd, except for the number 2; and the only reason that is the case is because two is only the second chronologic whole number…. So, the only options for it to be divided by (without getting a fraction) are 1 and 2.

Numerically, the first several prime numbers are:

2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. There are an infinite amount of prime numbers.

Let’s practice identifying prime numbers.

Is 9 a prime number? Well, it can be divided by 1 and by itself, but are there any other numbers it can be divided by? Yes. 3 goes into 9 three times.

What about 31? Is it a prime number? Yes. There is not another number other than 1 and itself that it can be divided by without getting a fraction!

Now, let’s take a look at prime factorization.

If you recall factors are any numbers that you multiply together to get another number.

Well, prime factorization uses this same concept, except you are only looking for the prime numbers that multiply together to get the original number.

**Here’s an example:**

**What are the prime factors of 24?**

The easiest way to start is by starting with the smallest prime numbers, which will always be 2, so let’s see if that works.

24 / 2 = 12

It did divide evenly, however 12 is not a prime number, so we must try to go even further.

Let’s try 3.

12 / 3 = 4

3 worked as well, but our result still isn’t a prime number. So, we must go even further.

Let’s try 2 again.

4 / 2 = 2

It worked! We’ve gone the furthest we can go.

So, our answer is 24 = 2 x 2 x 2 x 3, or it can be rewritten as 24 = 2^3 x 3.

Let’s look at another one.

**What is the prime factorization of 72?**

Let’s start with 2.

2 goes into 72, 36 times; but 36 is not a prime number. So, we must go further.

Let’s try 3 now. 3 goes into 36, 12 times; but 12 is not a prime number.

Let’s try 3 again. 3 goes into 12, 4 times; but, yet again, 4 is not a prime number. So, We need to go further.

2 goes into 4, 2 times.

Now, we have our answer.

72= 2 x 3 x 3 x 2 x 2

Or, we can rewrite this to be 72= 2^3 X 3^2

Spend some time practicing prime factorization on your own. Remember, when you write out your answer you are only concerned about the prime numbers that multiply together to get the original number.

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