# Prime factorization using repeated division

In these lessons and solutions, we will learn how to find prime factors using division.

The prime factors of a number are factors which are prime numbers. We can find the prime factors of a number by repetitive division or stacked division. To find the prime factorization of the number, we need to find the prime factors that when multiplied together gives the number.

Related Topics:
Prime Factorization using factor trees
More Arithmetic Lessons
Free Math Worksheets

Example:

Find the prime factors of 36.

The following diagrams show Prime Factorization using Factors Trees and using Repeated Division.

The prime factors of 36 are 2 and 3.

We can write 36 as a product of prime factors: 2 × 2 × 3 × 3

To find prime factors using the repetitive division, it is advisable to start with a small prime factor and continue the process with bigger prime factors.

Prime Factorization Using Stacked Division

This video provides two examples of how to use stacked division to find the prime factorization of a number rather than making a prime factorization tree.
A number is divisible by 2 if it is even or ends in 0, 2, 4, 6, 8.
A number is divisible by 3 if the sum of the digits is divisible by 3. A number is divisible by 5 if it ends in 0 or 5.
Example:
Use division to find the prime factorization.
a) 300
b) 693 Prime Factorization Using Stacked Division
Example:
Use division to find the prime factorization of 6,552.

Prime Factorization with Upside Down Division
Prime factors of a number can be found by using upside down division. Prime Factorization using Division Method
Example:
Find the prime factorization of the following by the division method
a) 12
b) 480 Prime Factorization with Upside Down Division Examples of prime factorization using repeated division

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.