How to Make a Factor Tree in 5 Easy Steps

A factor tree is a useful tool. Although it has many uses, it's especially handy when finding factors of large numbers. For smaller numbers, making a list and writing the factors out is a more convenient way to solve.

However, in trying to determine the factors for larger numbers, it's easier to route it out.

Learn how to make a factor tree and solve all of your math problems that involve finding the factors of any number.

Difficulty: Moderately Easy

Instructions

1. 
    
   Write the number you are factoring at the very top.

   Write the number you want to factor. In this example, we'll use 210. Write this number at the top of the paper you're using.
   
   Basically, the number is at the top and all of it's factors are branched out, underneath. Just like a real tree. So our first, top branch, is 210.

2. 
    
   Make sure to add the lines, one for each number, on each level of the factor tree. This keeps it like a graphic organizer.

   Make the second level of a factor tree. We pick any number that goes into 210 evenly. You can choose any number, but for this example, we use 2.
   
   What can we multiply X 2 and get 210? 105. So, the second level of our factor tree is 2 and 105.

3. 
    
   Move on to the next level of your factor tree by finding two numbers that go into the number from the level above.

   Continue to the next level. Since 2 can't be broken down any further, we leave it alone and concentrate on 105. What two numbers can be multiplied together to make 105?
   
   We know that 5 goes into 105, so we use it next. However, any number that goes into 105 evenly can be used.
   
   5 times what is 105? 21. So, on our third branch, we write 5 and 21.

4. 
    
   3 X 7 is 21, so 3 and 7 are the fourth level of the factor tree.

   Complete the fourth level of the factor tree, dealing with 5 and 21. We leave 5 alone, because it can't be broken down any further, and concentrate on 21. What 2 numbers can be multiplied together to get 21? 3 X 7, so our fourth level is 3 and 7.

5. 
    
   The factors of 210: 2,5,7,3.

   Write all the factors from the bottom row. Now, all of our bottom branches are 2,5,7,3.
   
   We are now finished with the factor tree, because none of these numbers can be broken down any further, except for 1, which doesn't count. So, the factors of 210: 2,5,7,3.
   
   Make sure, once you've finished your factor tree, to go back and grab all of the branches from above that ended, because they couldn't be broken down any further.

Tips & Warnings

• When you finish a factor tree, you should be able to multiply all the numbers and come up with your original number. In the case above, 210.

[1InternetSmarty]

on 5/1/2009 Impressive! Thanks for explaining how to make a factor three. Five stars.

[goodselfme]

on 4/28/2009 Thank you for explaining the factor tree so well.

[sonni57]

on 4/28/2009 I've never heard of a factor tree thanks for the good information.