Lesson: Greatest Common Factor

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Lesson Objective

SWBAT find the greatest common factor of two or more numbers with 80% accuracy.

Lesson Plan


6.NSO-N.6. Apply number theory concepts — including prime and composite numbers; prime factorization; greatest common factor; least common multiple; and divisibility rules for 2, 3, 4, 5, 6, 9, and 10 — to the solution of problems


Essential Question

SWBAT find the greatest common factor of two or more numbers with 80% accuracy.

Are all odd numbers prime numbers?



Lesson Agenda

Agenda Item/ Time (Board Configuration)

 5 E’s

Learning Activities



Teacher will do…

Students will do …

10 minutes

Daily Math Review (Warm-Up/ Do Now)

Find the prime factorization of each number.

1.       90

2.       72

3.       111

Complete the Do Now problems

5 minutes

Mental Vocabulary

Common Factor: factors that are the same for two or more numbers or expressions

Greatest common factor: the greatest of these common factors

Students will copy down and give and example/non example

10 minutes



Use a Venn diagram to show how to find the GCF:

Venn diagram’s use circles to represent collections of objects. The intersection, or overlap, of two circles indicates what is common to both collections.

example is on guided notes)


Students listen to directions and create a Venn Diagram




10 minutes



Explore (Conceptual Development)

Steps to find the GCF:

1. write the prime factorizations of all numbers

2. find the common factors.

3. multiply them to find the GCF.


Step to find the GCF:

1. write all factors for all integers

2. circle the largest factor both integers have in common.

Ex1: Find the GCF of 40 and 60 using both methods

Ex 2: Find the GCF of 12 and 87 using both metods

List the factors of 18 and 30


10 minutes




(Guided Practice)

A factor that two or more numbers share is a common factor


The greatest common factor (GCF) of two or more numbers is the greatest shared by all the numbers


Use a Venn diagram to show the factors of 24 and 60 then list the factors they have in common


Real world application: organizers for a high school graduation have set up chairs in two sections. They put 126 chairs for the graduates in the front section and 588 chairs for guests in the back section. If all rows have the same number of chairs, what is the greatest number of chairs possible for a row?

Actively listening and taking notes and participating when asked to do so.


15 minutes



Extend/ Elaborate


Give students the numbers 30 and 84 and have them find the GCF


Have students find the GCF for 5 other pairs using any method they prefer.

1.  10, 45  2. 25,100  3. 57, 84   4. 12, 18, and 36  5. 42, 65

Use Venn Diagrams to show the GCF of given numbers and answer the following:

1.  What do the numbers in the intersection (“the overlap”) of the circular regions have in common?

2.  List five numbers that fall in the region outside of the circles and explain why they belong outside of the circles?

3.  Explain how you can use your completed diagram to find the greatest factor that 30 and 84 have in common.  4.  What is the GCF?


10 minutes




(Assessment/ Closure)

Find the GCF of the following :

1. 63, 74                            2.  32, 48


3. Ms. Shear has 30 maple trees and 24 oak trees to plant. She wants to plant the same number of rows of maple and oak trees, and she wants to plant the greatest number of row that will divide evenly into both 30 and 24. What number of rows of trees should Ms. Shear plant?

a. 30

b. 24


d. 8



Complete exit slip


Workbook:  Practice 2-2 #’s 27-35


Factor, greatest common factor


Provide students with a multiplication grid or a table of the multiplication facts.  This will help them figure out the factors, or at least check once they have listed them.


Lesson Resources

GCF   Classwork


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