Factor Tree

A factor tree, also called a number tree, is a diagrammatic representation of all the factors of a number. The factors, when multiplied, give back the original number. 

It is particularly used to show the prime factorization of a number. Shown below is a factor tree showing the prime factorization of 36

Here, 2, 2, 3, and 3 are the prime factors of 36.
A factor is also used for simplifying fractions and finding the least common multiple (LCM) and greatest common factor (GCF). 

Note: We can also prime factor a number using the division method. 

Steps To Do

Here are the steps we follow to create a factor tree.

Step 1: Choosing the Number

Let us factor the number 72 using the factor tree

Step 2: Placing the Number on the Top of the Tree

We begin by placing 72 at the top of the tree, followed by two downward branches to write its two factors.

Step 3: Finding Two Factors

Next, we will think of two numbers that, when multiplied together, will give back the original number. 

For 72, we can use 8 × 9, as 8 × 9 = 72

Thus, 8 and 9 are the first two factors, which we will write below the branches.

Step 4. Splitting Each Composite Factor into Smaller Factors

Then, we will look at each factor and decide if it can be further divided into 2 more factors.

Here, 

8 is further split into 2 × 4, as 2 × 4 = 8 and

9 is further split into 3 × 3, as 3 × 3 = 9

Step 5. Continue Splitting Until All Numbers Are Prime

We further break each composite factor down into two factors.

Thus, 4 is split into 2 × 2, which are prime factors (as they cannot be divided any further)

Thus, 72 can be expressed as the product of its prime factors:

72 = 2 × 2 × 2 × 3 × 3

Here, the factor tree of 72 will look like this:

Solved Examples