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Factoring Numbers and GCF

I. Initial Planning

Content to be covered:
The content of this lesson begins with review of prime and composite numbers
and moves on to the definition of a factor and factor pairs. A factor game will be
introduced to enhance the lesson. Comparisons of different numbers and their factors
will lead to finding the greatest common factor by using the listing method .

Objectives:
• Students will be able to (SWBAT) define the term factor .
• SWBAT define the term factor pair and give examples.
• SWBAT play the Factor Game.
• SWBAT list the factors of two different numbers and compare them.
• SWBAT find the greatest common factor of two numbers using the listing
method.

North Carolina Standards
Competency Goal 1: The learner will understand and compute with rational numbers .
Objective 1.05: Develop fluency in the use of factors, multiples, exponential
notation, and prime factorization.
Objective 1.04: Develop fluency in multiplication and division of non - negative
rational numbers.
1.04 a: Analyze computational strategies

• Prior knowledge needed:
• Definitions of prime and composite numbers (This will be reviewed at the
beginning of the lesson.)
• Some comfort in identifying prime and composite numbers introduced in the
previous lesson
• Fluency with multiplication and division (tested for at beginning of unit)
• Internet knowledge
• Knowledge of the divisibility rules and how they apply (taught in lesson 3)

Materials needed:
• chalk board or dry erase board with chalk or dry erase markers
• computers
• overhead projector
• different colored pens/markers and pencils
• 3 different handouts that are front and back (shown below lesson plan)

Review

A ______________ is a number that can
______________ be divided evenly by one and itself.

Examples: 2, 3, 5, 7, 17, 23

A ______________ is a number that can be
divided evenly by numbers ______________ than one
and itself.

Examples: 4, 6, 8, 9, 15, 24, 32

New Stuff

What is a factor?

______________

______________

What are the factors of 2?

Factors of 3? Factors of 5? Factors of 4?
Factors of 6? Factors of 8? Factors of 12?

What is a factor pair?
(hint: pair means two!)

______________

______________

Examples:
3 and 4 are a factor pair of 12
2 and 3 are a factor pair of 6
4 and 5 are a factor pair of 20

How do I write out a factor pair?

Examples:

3 and 4 2 and 6 6 and 5
3,4 2,6 6,5

List two factor pairs of each number

a) 36 b) 20
c) 56 d) 24
e) 35 f) 40

More New Stuff

Let’s compare the factors of two different
numbers

1. List all factors of 24

2. List all factors of 36

What factors do they have in common?
These are called ______________

Definition of Greatest Common Factor (GCF):
The ______________ is the
______________ umber that divides _____________
(without a remainder) into each number in a set or
group
.

Examples:

1) Factors of 16: 1, 2, 4, 8, 16
Factors of 42: 1, 2, 6, 7, 14, 42
Common factors: 1 and 2 GCF: 2

2) Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Common factors: 1 and 5 GCF: 5

3) Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 8: 1, 2, 4, 8
Common factors: 1, 2, and 4 GCF: 4

Back to notes

What are the common factors of 24 and 36?
What is their greatest common factor?

Individual Exercises:
List the factors of each pair and circle the GCF .

1. 6 and 14 2) 4 and 10
3) 18 and 22 4) 26 and 13
5) 30 and 42 6) 48 and 56
7) 50 and 120 8) 70 and 130

Homework

1. List all factors for each of the following numbers.
Please write your answers using factor pairs.
(You may use your calculator )

a) 88 b) 96
c) 102 d) 120
e) 30 f) 95

2. List the factors of each set of numbers. Circle the
common factors and write down the GCF.

a) 76 and 52 b) 18 and 45
c) 72 and 48 d) 81 and 40
e) 29 and 87 f) 44 and 68

Extra Credit:

Write out all of the factor pairs for each number.

1) 188

2) 236

Find List the common factors and the GCF for the sets
of numbers below. (Hint: you will have to factor each
number first!)

1) 36, 12, and 42

2) 8, 40, and 32

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