How do you use prime factorization to find the GCF or

LCM of two whole numbers?

For example, how do you use prime factors to find the GCF and LCM of

8 and 30?

In this lesson you will learn how to find the GCF and LCM

of two whole numbers by using their prime factors.

Let’s Review

7 is a prime number. 7 x 1 = 7

Prime numbers have only two factors, one and themselves.

Composite numbers have more than two factors.

10 is a composite number. 1 x 10 = 10 2 x 5 = 10

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17…

Let’s Review

Prime factorization is finding a string of prime numbers that when multiplied result in your

original number.40

factor tree

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17…

2 x 20

2 x 10

2 x 5

40 = 2 x 2 x 2 x 5

All composite numbers can be written as a string of

prime factors.

A Common Misunderstanding

Confusing factors with multiples

Find the factors of 25.

25, 50, 75…1, 5, 25

A Common Misunderstanding

Remembering to find only prime factors for a number when using prime

factorization.

The prime factors of 20 are 2 x 10.

Core Lesson

How do you use prime factorization to find the GCF and LCM of 8 and 30?

8factor tree

2 x 4

2 x 2

= 2 x 2 x 2 30

2 x 15

3 x 5

= 2 x 3 x 5

Core Lesson

8= 2 x 2 x 2 30= 2 x 3 x 5

Venn Diagram

22 2 3 5

GCF

LCM

The GCF of 8 and

30 is 2.

The LCM of 8 and 30 is 120.

2 x 2 x 2 x 3 x 5 = 120

Core Lesson

What is the GCF and LCM of 18 and 27?

18

2 x 9

= 2 x 3 x 3 27

3 x 9

3 x 3

= 3 x 3 x 3

3 x 3

Core Lesson

18= 2 x 3 x 3 27= 3 x 3 x 3

Venn Diagram

3 3

GCF

LCM

The GCF of 18 and 27 is 9.

The LCM of 8 and 30 is 54.

2 x 3 x 3 x 3 = 54

3

3 x 3 = 9

2

In this lesson you have learned how to find the GCF and LCM of

two whole numbers by using their prime factors.