The Factor Tree method is a simple way to break down the given numbers into prime factors. It is written in such a way that you get the exact divisibility by using the prime factors of the original number. Students who are unable to understand the concept of the Factor Tree Method can make use of this article and practice the problems. You can see questions with clear-cut solutions in the below section. Know how to solve the multiples using the Factor Tree Method from this page.

**Refer:**

- Methods of Prime Factorization
- Worksheet on Methods of Prime Factorization
- Factors
- Properties of Multiples

## Factor Tree – Definition

A factor tree is a diagram where we can find the factors of a number, from that we can find the factors of those numbers till we get the prime factors for the given number.

For example, let us see how to find the prime factors of 12.

**Solution:**

First split the numbers into factor pairs.

12 can be written as 4 × 3.

12 = 2 × 2 × 3

The prime factors of 12 are 2 and 3.

### How to do Prime Factorization using the Factor Tree Method?

The factor Tree Method is one of the simple ways to find the prime factors of the original number. There are some to step to solve the problems using a factor tree method.

1. The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring.

2. Check whether 2 is a factor of the given number.

3. Break down each set into factors.

4. Check for other prime numbers like 3, 5 factors of the original number.

5. Then split the factors until you get all the prime factors.

6. At last write the prime factors of the original number.

### Factor Trees Examples

**Example 1.**

Find the factors of 24.

**Solution:
**Use Factor Tree Method to find the factors of 24.

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring.

Write the factors of 24

Break down each set into factors.

Then split the factors until you get all the prime factors.

12 can be written as 2 × 12

2 is a prime number. So split 12 into 2 × 6

2 is a prime number. So split 6 into 2 × 2

24 = 2 × 2 × 2 × 3

Thus the prime factors of 24 are 2, 2, 2, 3.

**Example 2.**

Find the factors of 36

**Solution:
**Use Factor Tree Method to find the factors of 36.

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring.

Write the factors of 36

4 × 9

Break down each set into factors.

Then split the factors until you get all the prime factors.

Split 4 into 2 × 2

Split 9 into 3 × 3

36 = 2 × 2 × 3 × 3

Thus the prime factors of 36 are 2, 2, 3, 3.

**Example 3.**

Find the factors of 25

**Solution:
**Use Factor Tree Method to find the factors of 25.

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring.

Break down each set into factors.

Write the factors of 25

25 = 5 × 5

5 is a prime number.

Thus the prime factors of 25 are 5, 5.

**Example 4.**

Find the factors of 32

**Solution:**

Use Factor Tree Method to find the factors of 32.

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring.

Write the factors of 32.

Break down each set into factors.

Then split the factors until you get all the prime factors.

32 can be written as 8 × 4

8 can be written as 4 × 2

4 can be written as 2 × 2

The factors of 32 are 2 × 2 × 2 × 2 × 2

Thus the prime factors of 32 are 2, 2, 2, 2, 2.

**Example 5.**

Find the factors of 48

**Solution:**

Use Factor Tree Method to find the factors of 48.

The first step in making a factor tree is to find a pair of factors whose product is the number that we are factoring.

Write the factors of 48.

Break down each set into factors.

Then split the factors until you get all the prime factors.

48 can be written as 4 × 12

Split the factor pairs

4 = 2 × 2

12 × 2 × 6

6 can be written as 2 × 3

Thus the factors of 48 are 2 × 2 × 2 × 2 × 3

Thus the prime factors of 48 are 2 and 3.

### FAQs on Factor Tree Method

**1. What is a Factor Tree?**

One method for producing the prime factorization of a natural number is called a factor tree.

**2. How to make a factor tree?**

1. First write the given number

2. Find a pair of factors

3. Break down each set into its own factors.

4. Repeat until you reach nothing but prime numbers.

**3. What is the factor tree of 27?**