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…

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 , 50, 75… 1, 5, 25

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? 8 factor tree 2 x 4 2 x 2 = 2 x 2 x x 15 3 x 5 = 2 x 3 x 5

8 = 2 x 2 x 2 30 = 2 x 3 x 5 Venn Diagram GCF LCM The GCF of 8 and 30 is 2. The LCM of 8 and 30 is 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 x 9 3 x 3 = 3 x 3 x 3 3 x 3

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 x 3 x 3 x 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.