Home | Math | Prime Factorization with Prime Factor Trees

# Prime Factorization with Prime Factor Trees

November 8, 2023
written by Rida Mirza

Prime factorization is a fundamental concept in mathematics that allows us to break down a number into its prime factors.

In this article, we will explore prime factorization using a visual tool called “Prime Factor Trees.”

## What is Prime Factorization?

Prime factorization is the process of expressing a number as the product of its prime factors. Prime factors are the building blocks of all numbers.

## How to Create a Prime Factor Tree

Creating a prime factor tree is a visual way to find the prime factors of a number. Here’s how you can do it:

• Start with a Number: Begin with the number you want to factorize. For example, let’s take the number 36.
• Find Two Factors: Identify two numbers that multiply to give you the original number. In our example, 36 can be divided into 6 and 6, which are 2 x 18.
• Continue Factoring: Repeat this process for each factor until you can no longer divide. For 18, you can split it into 2 and 9, which are 2 x 3 x 3.
• Draw the Tree: Create a tree-like diagram with branches for each factorization step. It should look like this:

## Solved Examples

### Example 1

Prime Factorization of 48

• Divide it into 2 and 24 (2 x 24).
• Continue factoring 24 into 2 and 12 (2 x 12).
• Further factor 12 into 2 and 6 (2 x 6).
• Finally, 6 can be split into 2 and 3 (2 x 3).

So, the prime factors of 48 are 2 x 2 x 2 x 2 x 3.

### Example 2

Prime Factorization of 90

• Divide it into 2 and 45 (2 x 45).
• Continue factoring 45 into 3 and 15 (3 x 15).
• Further factor 15 into 3 and 5 (3 x 5).

The prime factors of 90 are 2 x 3 x 3 x 5.

## FAQs

### Why is prime factorization important?

Prime factorization is essential for various mathematical problems, including simplifying fractions, finding the greatest common divisor, and understanding number properties.

### Can you factorize a prime number?

No, prime numbers have only two factors: 1 and themselves. They cannot be further factorized.

### What is the relationship between prime factors and the original number?

The original number is the product of its prime factors. By finding prime factors, you can understand how a number is composed.

File Under: