__Objectives:__

At the end of the lesson, students should be able to write the prime factors of any given number.

A **PRIME NUMBER** is a number than can only be divided by 1 and itself.

If a factor is a prime number, it is also called a PRIME FACTOR.

The best way to find the prime factors of a given number is by dividing it by the smallest prime number then moving on to larger prime numbers that can divide the number.

Let’s explore various ways of finding the prime factors of a number.

__Example 1:__

Find the prime factors of 15

15 = 1 x 15

= 3 x 5

Factors = {1, 3, 5, 15}

Prime factors = {3, 5}

__Example 2:__

Find the prime factors of 24

From the example above, 24 is divided by 2, which is a prime number giving you the answer of 12. 12 can be divided by 2 or 3 i.e.

Both answers are not prime numbers, so they are further divided by prime numbers till they can no longer be divided. After this, all the prime factors are listed.

Note that a “x” sign is placed between the factors because they are actually multiplying each other.

__Example 3:__

List the prime factors of 20

**Note: 1 is not a prime number and 2 is the only even number.**

__Example 4:__

Find the prime factors of these numbers using the ladder method.

- 20
- 50

__Solution__

a) 20 =

b) 50 =

From the example above, two columns are created and the number whose factors are being listed is written on the top right column. The prime factors are then written out on the left column and used to divide the numbers until a number that cannot be divided further is obtained.

The prime factors are then listed.

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