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.
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.
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.
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…
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.
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.
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.