# Prime Factorization Using Repeated Division

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

### What Are Prime Factors

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.

Example:
Find the prime factors of 36.
The following diagrams show Prime Factorization of a number using Factors Trees and using Repeated Division. Scroll down the page for more examples and solutions of prime factorization.

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

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 with Upside Down Division

Example:
Find the prime factorization of the 210 by the division method.

Examples of prime factorization using repeated division

6, 24, 35, 51

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