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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:
image showing prime factor tree

Solved Examples

Example 1

Prime Factorization of 48

image of 48 prime factor tree

  • Start with 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

image of 90 prime factor tree

  • Start with 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.


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.

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