Login
Copyright

How to Find the Prime Factorization of a Number

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Find the Greatest Common Factor

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:07 Factors of a Number
  • 1:11 Prime Numbers
  • 1:28 Prime Factorization
  • 1:40 How to Determine the…
  • 5:00 Lesson Summary
Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!
Create An Account

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Jennifer Beddoe
The prime factorization of a number involves breaking that number down to its smallest parts. This lesson will show you two different ways to discover the prime factorization of any number.

Factors of a Number

When you are trying to come to a conclusion about a problem, you often say that there are many 'factors' to consider. This means that there are many parts that make up the whole problem of what you are trying to decide. If the decision is where to go for dinner, the factors involved in that decision might be price, how far away the restaurant is, and how well you will enjoy the food.

Numbers also have factors, the parts that make up the whole number. The factors of a number are the numbers that, when multiplied together, make up the original number.

For example, factors of 8 could be 2 and 4 because 2 * 4 is 8.

And factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24, because 1 * 24 is 24, 2 * 12 is 24, 3 * 8 is 24 and so is 4 * 6. So all of these numbers are said to be factors of 24.

Prime Numbers

A prime number is any number that is only divisible by itself and 1. Some examples of prime numbers include 2, 5 and 17. Numbers such as 15 or 21 are not prime, because they are divisible by more than just themselves and 1.

Prime Factorization

To factor a number is to break that number down into smaller parts. To find the prime factorization of a number, you need to break that number down to its prime factors.

How to Determine the Prime Factorization of a Number

There are two main ways for determining the prime factors of a number. I will demonstrate both methods, and let you decide which you like best.

Both methods start out with a factor tree. A factor tree is a diagram that is used to break down a number into its factors until all the numbers left are prime.

The first way you can use a factor tree to find the factorization of a number is to divide out prime numbers only. Let's factor 24 using this method.

Since 24 is an even number, the first prime number that can be factored out is a 2. This leaves us with 2 * 12. Again, 12 is an even number, so we can factor out another 2, leaving us with 2 * 2 * 6. Since 6 is even, we can factor out a third two, leaving 2 * 2 * 2 * 3.

null

All of these numbers are prime, so the factorization is complete.

The other method for using a factor tree to find the prime factorization of a number is just to pull out the first factors that you see, whether they are prime or not. Looking back at our example from above, let's factor 24 again using this method.

The first thing you might notice is that 6 * 4 is 24, so that is one set of factors for 24. Since neither of these numbers are prime, we can continue to factor both of them. 6 can be broken down to 2 * 3, and 4 can be broken down to 2 * 2. Now all of our factors are prime, and the factorization of 24 is complete, again giving the answer of 2 * 2 * 2 * 3.

null

Both of these methods work equally well, and can be used interchangeably. There are people who like to use certain tricks to pull out prime numbers first without having to decide what other numbers might be factors of the original number.

The tricks to find some of the prime numbers are:

To unlock this lesson you must be a Study.com Member.
Create your account

Register for a free trial

Are you a student or a teacher?
I am a teacher
What is your educational goal?
 Back

Unlock Your Education

See for yourself why 10 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back

Earning College Credit

Did you know… We have over 79 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it free for 5 days!
Create An Account
Support