Page 138 - Math Course 1 (Book 1)

Greatest Common Factor (GCF)

Mo. 4

Lesson 4

KEY CONCEPTS: Let’s Begin
1. Find the greatest common factor of two or
more numbers or monomials.
2. Use the Distributive Property to factor
algebraic expressions. Find The GCF

Examples
MO. 4 - L4a
Finding the GCF of Find the GCF of 16 and 24.

Monomials Method 1 List the factors.
factors of 16: 1, 2, 4, 8, 16
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Vocabulary A-Z The greatest common factor

Let us learn some vocabulary Answer of 16 and 24 is 8.

Find the GCF of 16 and 24.

Venn Diagram Method 2 Use prime factorization.
16: 2 • 2 • 2 • 2 Common factors of 16 and
the relationships among sets of numbers or objects 24: 2 • 2 • 2 • 3 24: 2, 2, 2
by using overlapping circles
The GCF is the product of the common prime
Prime Factors of 12 Prime Factors of 20 factors.

2 • 2 • 2 = 8

3 2 5 Again, the GCF of 16 and 24 is 8.
2

Answer 8

12 = 2 • 2 • 3 20 = 2 • 2 • 5 Find the GCF of 28 and 35.

Greatest Common Factor First, factor each number completely. Then circle
the common factors.
The greatest number that is a factor of two or more 28: 2 • 2 • 7
numbers is called the greatest common factor (GCF). 35: 5 • 7

factors of 12: 1, 2, 3, 4, 6, 12 The common prime factor is 7.
factors of 20: 1, 2, 3, 4, 5, 10, 20

Answer The GCF of 28 and 35 is 7.
Common factors of
12 and 20: 1, 2, 4

The greatest common factor of 12 and 20 is 4.

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