Definitions:

Common Factors – Are factors shared by two or more whole numbers.Greatest Common Factor (GCF) – Is the largest common factor shared between two or more whole numbers.

Example 1: Find the GCF of 16 and 24 by listing the factors.

Factors of 16: 1, 2, 4, 8, and 16

Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24

8 is the largest common factor; therefore, it is the GCF of 16 and 24.

Method 1: Finding The GCF by Listing the Factors

Strategy:1.) List the factors of each number.2.) Identify the common factor of the numbers that is the greatest.

Example 2: Find the GCF of 40 and 12 by using primefactorization. 40 12

5 8 6 2 2 4 3 2 2 2 5 • 2 • 2 • 2 3 • 2 • 2 2 • 2 = 4

Method 2: Finding The GCF by Using Prime Factorization

Prime Factorization

Product of the common prime numbers. 4 is the GCF.

Strategy:1.) Find the prime factorization of each number.2.) Identify the common prime factors.3.) Then, multiply the common prime factors.

Example 3: Find the GCF of 45 and 75 by making a table.

Method 3: Finding The GCF by Using a Table

Strategy:1.) Set up a table.2.) Write a prime number in the left column that at ALL of the numbers in the problem are divisible by.3.) Then, divide each number by that prime number.

4.) Continue this process until there aren’t any more numbers that go into ALL of the numbers in the problem.5.) Lastly, multiply all of the prime numbers that you’ve used. That product is the GCF.

3 • 5 = 15Multiply the prime numbers. 15 is the GCF of 45 and 75.

Prime Numbers 3 45 75 5 15 25

3 5

Find the GCF of the following whole numbers by using prime factorization.

1.) 45 and 18 2.) 36 and 84

Find the GCF of the following whole numbers by using the table.

1.) 28 and 42 2.) 18, 27, and 30

Real-Life Application

There are 12 boys and 18 girls in Ms. Ruiz’s science class. The students must form lab groups. Each group must have the same number of boys and girls. What is the greatest number of groups Ms. Ruiz can make if every student must be in a group?