The Greatest
Common Factor
Instructional Treatment #1
Introduction
Are you ready to start learning more than you
already know about fractions? If so, you must
remember that in order to get to the end you must
start at the beginning. That means you start with the
basics.
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What Am I Going to Learn?
In this first lesson you will:
•Briefly review what factors are
•Learn how to find the greatest common factor
and why it is important
•Practice some examples on your own
*At anytime during this lesson, you may
take notes to help you remember any
important information. You will be having a
discussion at the end with your group
members.
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Pop Quiz
What is a factor?
A factor is any number that when added together
gives you the sum (or answer).
TRUE FALSE
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Back
Factors
First, you must remember what factors are.
Factors are the numbers that when multiplied
together give you the product (or answer).
For example:
3 x 4 = 12
3 and 4 are factors of 12
Find out more about factors!
Try finding factors on your own, click here!
(maximum amount of time at this site: 5 minutes)
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Greatest Common Factor
Now that you have remembered what factors are,
it’s time to learn about the greatest common
factor (GCF).
The GCF is the factor with the highest value found
in all of the numbers that are being factored.
For example: the GCF of 12 and 36 is 12.
12: 1, 2, 3, 4, 6, 12
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Sure, the numbers 1, 2, 3, 4, and 6 are common,
but they are NOT the highest value.
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Why is the GCF important?
The GCF is important to know when it comes to
reducing your fractions. When you reduce your
fractions, you find all of the equivalent fractions to
the fraction you started out with.
Just keep this in mind, you will learn about
reducing later.
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More About the GCF!
1. Read this about the GCF!
2. Watch this! Click on the screen below to
start.
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How to Find the GCF
Now it’s your turn to find the GCF. There are two
methods to choose from that will help you find the
GCF. You can list them in a straight line horizontally
or list them in a T-chart.
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How to Find the GCF: Method 1
Step 1: Write down one of the numbers that is being factored.
Step 2: Find ALL of the factors of that number and list them in order. (If
you were to draw arrows from one number to its match, it would look like
you have drawn a rainbow.
Step 3: Find all of the factors for the other number by following steps 1 &
2.
Step 4: Find the same number in each set of factors that has the highest
value.
Factors that are found in
12: 1, 2, 3, 4, 6, 12 both numbers are 1, 2, 3,
4, 6, and 12, but 12 is the
GCF because it has the
highest value.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
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How to Find the GCF: Method 2
Step 1: Draw yourself two different T-charts and put the number that is
going to be factored at the top (one number on each chart).
Step 2: On each row underneath the number, pair up the factors that
when multiplied together equal the number at the top.
Step 3: On each T-chart, find all of the common factors and circle them.
Step 4: Find the same number in each set of factors that has the highest
value.
The common numbers that were
circled were 1, 2, 3, 4, 6, and 12.
The GCF is 12 because it is the
number with the highest value.
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Your Turn!
Now it’s time for you to practice. Choose one of the two methods to help
you find the GCF of each set of numbers. When you have finished, click on
the answer key to check. If you forget how to use one of the methods, click
on the buttons below.
1) 3 and 9
2) 15 and 21
3) 6 and 45
4) 7 and 61
5) 32 and 54
Answer Key Method 1~List Method 2~T-chart
Answer Key
1) GCF is 3
2) GCF is 3
3) GCF is 3
4) GCF is 1
5) GCF is 2
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How to Find the GCF: Method 1
Step 1: Write down one of the numbers that is being factored.
Step 2: Find ALL of the factors of that number and list them in order. (If
you were to draw arrows from one number to its match, it would look like
you have drawn a rainbow.
Step 3: Find all of the factors for the other number by following steps 1 &
2.
Step 4: Find the same number in each set of factors that has the highest
value.
Factors that are found in
12: 1, 2, 3, 4, 6, 12 both numbers are 1, 2, 3,
4, 6, and 12, but 12 is the
GCF because it has the
highest value.
36: 1, 2, 3, 4, 6, 9, 12, 18, 36
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How to Find the GCF: Method 2
Step 1: Draw yourself two different T-charts and put the number that is
going to be factored at the top (one number on each chart).
Step 2: On each row underneath the number, pair up the factors that
when multiplied together equal the number at the top.
Step 3: On each T-chart, find all of the common factors and circle them.
Step 4: Find the same number in each set of factors that has the highest
value.
The common numbers that were
circled were 1, 2, 3, 4, 6, and 12.
The GCF is 12 because it is the
number with the highest value.
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What Now?
It’s time to get with your group members.
• Discuss what factors are, what the GCF is and why it is important,
how to find the GCF.
• Each group member is to come up with their own problem for the
other group members to try. Each member chooses one set of two
numbers and works out the problem to find the answer their group
members should get. Then each group member will try each
other’s problem. Share answers after everyone has tried ALL
problems.
• If everyone in your group gets all answers correct, you’re done.
If not, help them to understand where they made a mistake.
• See your teacher.
NEXT LESSON: HOW TO FIND THE LEAST COMMON MULTIPLE