The Factor Tree | Elementary

The Factor Tree - Cycle 2

| Mathematics

What is a factor tree used for?

The factor tree makes it possible to find the prime factors and the prime factorization of a number.

To find out what prime factors and prime factorization are, you can read the concept sheet Prime Factors and Prime Factorization.

Rule

To make a factor tree, I have to follow these steps.

I write the number to be decomposed.
I find two factors that, when multiplied together, give the starting number. I write them at the end of two branches.
I decompose the factors which are not prime by writing their factors at the end of two new branches.
I continue until all the factors at the end of the branches are prime.
I write the prime factorization of the number as a multiplication equation, using the prime factors at the end of each of the tree branches.

Example

What is the prime factorization of the number 72?

I write the number to be decomposed.
I find two factors that, when multiplied together, give the starting number. 6 × 12 = 72 I write them at the end of the two branches.
I decompose the factors which are not prime by writing their factors at the end of two new branches. 2 × 3 = 6 3 × 4 = 12
I continue until all the factors at the end of the branches are prime. 2 × 2 = 4
I write the prime factorization of the number as a multiplication equation, using the prime factors at the end of each of the tree branches.

2 × 3 × 3 × 2 × is the prime factorization of the number 72.