I think factor trees are one of the coolest “tools” for middle school students!  Students tend to like them and they have several different uses in middle school math.

Here are the 5 ways I use factor trees with my students:

1.  Prime Factorization
This is the most obvious use of factor trees and it’s typically the first way students learn to use them.

When I teach prime factorization I introduce the idea of the Fundamental Theorem of Arithmetic (no matter how many different factor trees students make for a number, they will always get the same prime factorization).  I also emphasize the two things they can/should do to check their answer:
– make sure all numbers in their prime factorization are PRIME numbers
– make sure the product of the numbers in their prime factorization is the starting number

2 & 3.  GCF and LCM
Using factor trees is my second favorite way to teach the greatest common factor and least common multiple of numbers and/or monomials.  (The cake method is my favorite method).

4.  Simplifying Radicals
Factor trees make simplifying radicals so easy for my pre-algebra and algebra students!  Students understand that finding the square root of a number means figuring out what number times itself equals the starting number, so in simplifying radicals they are simply pulling out one of each prime factor that is listed twice in the factor tree.

5.  Factoring Trinomials
The idea behind factoring trinomials is pretty simple.  Students need to come up with two numbers that have a certain product and sum.  Students are typically pretty good at factoring simple trinomials like this, since coming up with the two numbers is a breeze:

But, many students struggle with problems like the one below, not because they don’t understand the factoring process, but because they can’t come up with the two numbers with the given sum and product.   That’s where factor trees come in handy!

For students who have a tough time coming up with the numbers, I have them make a factor tree for 126.  Once they have it broken into its prime factors, they just need to break up the prime factors into 2 numbers every possible way until they find the ones with a sum of 23.

While this method does take some trial and error, it gives “stuck” students a starting place and a set number of possibilities to try.

Do you use factor trees in any other ways in your math classes?  If so, please share!

Thanks for reading,
Christina