Lesson 3-3

For Example 5 Find Common Factors
a. Find 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.

For Example 6 Find the Greatest Common Factor
b. Find the greatest common factor (GCF) of 48 and 64.

List the factors of 48 and 64.

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. 
The GCF of 48 and 64 is 16.

You can 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.

c. Find the GCF of 24 and 42by using prime factors.

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.  
The GCF of 24 and 42 is 2 × 3 or 6.

Example 7 Write Fractions in Simplest Form
d. Write  in simplest form.
 
[Set 3 in red (and circle) in both lists]
12: 1, 2, 3, 4, 6, 12	
15: 1, 3, 5, 15	List the factors. Find the GCF.

[stack 12 ÷ 3 and 15 ÷ 3. stack 4 and 5]
12 ÷  ÷ 3 = 	Divide both numerator and denominator by the GCF.	

 =  in simplest form.

For Example 8 
e. [Real-World] STUDENTS   In a class of 42 students, 28 of them participate in after-school sports activities. Express the fraction  in simplest form.   
The GCF of 28 and 42 is 14.

 = 	Divide both the numerator and denominator by the GCF.
	
2 out of every 3 students, or  students, participate in after-school sports activities.