Title: Lesson 5-1
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 4-1

Example 1 Identify Common Factors
Identify the common factors of 18 and 45.

First, list the factors by pairs for each number.
Factors of 18

1 × 18
2 × 9
3 × 6

Factors of 45

1 × 45
3 × 15
5 × 9

Circle the common factors.

The common factors are 1, 3, and 9.

Example 2 Find the GCF by Listing Factors
Find the GCF of 48 and 64.

First, make an organized list of the factors for each number.

48: 1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8 → 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
64: 1 × 64, 2 × 32, 4 × 16, 8 × 8 → 1, 2, 4, 8, 16, 32, 64

The common factors are 1, 2, 4, 8, and 16, and the greatest of these is 16. 
So, the greatest common factor or GCF of 48 and 64 is 16.

Use a Venn diagram to show the factors. 
Notice that the factors 1, 2, 4, 8, and 16 		
are the common factors of 48 and 64, and 
the GCF is 16.

Example 3 Find the GCF by Using Prime Factors
Find the GCF of 24 and 42.

METHOD 1  Write the prime factorization.

2 and 3 are common factors.

METHOD 2 Divide by prime numbers.

Divide both 24 and 42 by 2. Then divide the quotients by 3.

Using either method, the common prime factors are 2 and 3.  
So, the GCF of 24 and 42 is 2 × 3 or 6.

Real-World EXAMPLE
Example 4 Use the GCF to Solve a Problem
Mrs. Eakin’s Sweatshirt Money
Monday | $32
Tuesday | $64
Wednesday | $48
MONEY   Mrs. Eakin recorded the amount of money collected from students for school sweatshirts. Each student ordered one sweatshirt and paid the same amount. What is the most each sweatshirt could cost?

List all the factors of each number. Then find the greatest common factor.

factors of 32:  1, 2, 4, 8, 16, 32
factors of 64:  1, 2, 4, 8, 16, 32, 64
factors of 48:  1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The GCF of 32, 64, and 48 is 16. So, the most each sweatshirt could cost is $16.

Example 5 Use the GCF to Solve a Problem
How many students have ordered a sweatshirt if the cost of each shirt is $16?

There is a total of $32 + $64 + $48 or $144. So, the number of students that have ordered a sweatshirt is $144 ÷ $16 or 9.