What is a Factor Tree?

The definition of a factor tree is as follows:  A Factor Tree is a diagram used to break down a number by dividing it by its factors until all the numbers left are prime. This is useful for elementary school math for figuring out the greatest common factor between two numbers.

We start with what a prime number is: A prime number is a number that is only divisible by itself and the number 1.   The number 2 is the only even prime number. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …

Let’s tackle the number 4 and break it down into it’s factors.

Factor Tree of 4

This is our first Factor Tree! We took the number four and divided its factors until all the numbers that were left are prime (2 and 2).

Let’s tackle the number 6 and break it down into it’s factors.

Factor Tree of 6

Our second Factor Tree shows us that we can break 6 into two prime numbers, two and three.

So far we have encountered trees with one level of branches. Now from here on in it gets trickier.

Let’s tackle the number 8 now and see how we can break it down into it’s factors.

Factor Tree of 8 - Partial

We see that on our first division we get to 4 and 2.  The issue is that 4 is not a prime factor!  We have to continue the tree branches until we have all prime factors.  So we continue…

Factor Tree of 8 - Full

There we go!  All of our factors in the bottom branch of the Factor Tree are prime!  Let’s try a bigger number like 42.

Factor Tree of 42 - Example 1

Fantastic, we are able to get to all of our prime factors by the second row.  Wait a second you say!  Isn’t 42 divisible by 6? Why yes it is, let’s try to see what that Factor Tree would look like.

Factor Tree of 42 - Example 2

Amazing, right?  We are able to take our original number 42 and by dividing it another way we can still come up with the same Factor Tree factors.

Growing up this fascinated many of us here at theFactorTree.com so we named our company after one of our favorite concepts from Elementary/Middle School Mathematics.

Comments 28 Comments
Categories Fun, Math Tidbits
Author Sebastian
This entry was posted in Fun, Math Tidbits and tagged . Bookmark the permalink.

28 Responses to What is a Factor Tree?

  1. ann says, on May 9, 2012 at 6:41 pm:

    awesome it really helped

    • carlos says, on October 9, 2012 at 5:08 pm:


  2. Queen of Sneaks says, on July 26, 2012 at 5:53 pm:

    Wow, thanks. I NEVER understood this as well as I do now. ;D

  3. tykiyah says, on August 10, 2012 at 11:45 pm:

    math is fun

  4. Neeka Maraj says, on September 6, 2012 at 11:36 pm:

    At first i didnt get it but i totally get it now

  5. billy says, on September 16, 2012 at 8:23 pm:

    thanks really helpful

  6. zoey says, on October 9, 2012 at 7:18 pm:

    thank you you saved my math grade and my home work

    • paisly says, on November 28, 2012 at 11:46 pm:

      thx’s i really needed it

    • Brianna says, on January 8, 2013 at 9:36 pm:

      thanks U saved me and my math grade

  7. emily says, on October 9, 2012 at 11:28 pm:

    thats awesome thanks

  8. dan25000 says, on October 25, 2012 at 10:08 pm:

    I LOVE YOUR IMFOMATION!!!!!!!!!!!!!!!

  9. STEPHEN says, on October 31, 2012 at 6:03 pm:

    This site is helping we teachers in Ghana.We are very grateful

  10. Queen of France says, on November 1, 2012 at 7:45 pm:

    Good Job. Quite Decent I Find.

  11. Ivana says, on November 6, 2012 at 12:23 am:

    thanks it is very helpful

  12. Tom says, on November 7, 2012 at 12:14 am:

    Thanks, your explanation saved me a lot of time!

  13. Khoa says, on November 13, 2012 at 2:57 am:

    this really help me on my homework thanks

  14. h says, on November 29, 2012 at 2:20 pm:

    it helped in a project.

  15. robert sammarone says, on November 30, 2012 at 1:43 am:

    what if tou have a number like 13.how do you do the tree

  16. ryder says, on December 4, 2012 at 11:16 pm:

    I never new this. This really helped A LOT!!!!!!!!!!!!

  17. Jake says, on December 6, 2012 at 12:09 am:

    Saved me a lot of time.now i under stand it!thanks!!!

  18. Sheryl says, on December 7, 2012 at 9:12 pm:

    It really helped, as a definition

  19. Sheryl says, on December 7, 2012 at 9:12 pm:

    It also helped me on a question on an assignment I needed help from

  20. Bless says, on December 8, 2012 at 8:57 pm:

    thxs dued this was the last part i needed for my math project and i forgot all this stuff and it really helped!!:)

  21. Anna says, on January 4, 2013 at 9:51 pm:

    thank you this will really help me on my test

  22. Chloe says, on January 16, 2013 at 11:07 pm:

    Thanks it really helped

  23. Jason says, on July 12, 2013 at 7:53 am:

    Thanks! Now i understand! Thanks for the information!:)

  24. Allicsnah says, on July 18, 2013 at 1:47 am:

    This really helps me understand better.Now i can do this in my exams without any difficulties.

  25. Allicsnah says, on July 18, 2013 at 1:48 am:


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