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

**Related Pages**

Prime Factorization Using Factor Trees

Integers

Highest Common Factor

More Arithmetic Lessons

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.

Examples of how to use stacked division to find the prime factorization of a number rather than making a prime factorization tree.

Helpful Divisibility Rules

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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