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Objective
Find the greatest common factor (GCF)
of two or more numbers
Vocabulary
Venn diagram
The use of circles to show how elements
among sets of numbers or objects are related
Vocabulary
Greatest common factor (GCF)
The greatest of the common factors of two or
more numbers
Example 1 Find the GCF by Listing Factors
Example 2 Find the GCF Using Prime Factors
Example 3 Find the GCF Using Prime Factors
Example 4 Find the GCF of an Algebraic Expression
Example 5 Use the GCF to Solve a Problem
Find the GCF of 28 and 42.
Prime factor both 28 and 42
2 28
2 14
7
2 42
3 21
7
Circle factors that are common in each number then
write the common factor
2  7
Answer: GCF = 14
Multiply the common
factors
Identify as GCF
1/5
Find the GCF of 18 and 45
Answer: GCF = 9
1/5
Find the GCF of 20 and 32.
Prime factor both 20 and 32
2 20
2 10
5
2 32
2 16
2 8
2 4
2
Circle factors that are common in
each number and write as factors
Multiply the common
22
Answer: GCF = 4
factors
Identify as GCF
2/5
Find the GCF of 24 and 36.
Answer: GCF = 12
2/5
Find the GCF of 21, 42, and 63.
Prime factor 21, 42 and 63
3 21
7
3 63
3 21
7
2 42
3 21
7
Circle factors that are common in
each number and write as factors
37
Multiply the common
factors
Identify as GCF
Answer: GCF = 21
3/5
Find the GCF of 24, 48, and 60.
Answer: GCF = 12
3/5
ALGEBRA Find the GCF of 12p2 and 30p3
Prime factor 12p2 and 30p3
Multiply the
common
2
3
12p
30p
2
2
factors that are
2 6p2
numbers
3 15p3
3 3p2
5 5p3
Multiply the
2
3
p p
p
common
p
p
factors that are
2
p
p
same
p variables
Circle factors that are common in
each number and write as factors
23 p p
Identify as GCF
Answer: GCF = 6
6p2
4/5
ALGEBRA Find the GCF of
Answer: GCF = 7mn
4/5
ART Cindy wants to cut a 15-centimeter by
25-centimeter piece of tag board into squares for an
art project. She does not want to waste any of the tag
board and she wants the largest squares possible.
What is the length of the side of the squares she
should use?
Find the GCF of length of the tag board
3 15
5 25
5
5
Circle factors that are common in
each number and write as factors
GCF = 5
There are no other
common factors
Identify as GCF
5/5
ART Cindy wants to cut a 15-centimeter by
25-centimeter piece of tag board into squares for an
art project. She does not want to waste any of the tag
board and she wants the largest squares possible.
What is the length of the side of the squares she
should use?
GCF = 5 cm
Add dimensional
analysis
Answer: Cindy should use squares with
sides measuring 5 centimeters
5/5
*
CANDY Alice is making candy baskets using
chocolate hearts and lollipops. She has 32 chocolate
hearts and 48 lollipops. She wants to have an equal
number of chocolate hearts and lollipops in each
basket. Find the greatest number of chocolate hearts
and lollipops Alice can put in each basket.
Answer: 16 chocolate hearts and lollipops in each basket
5/5
Lesson 5:2
Assignment
Greatest Common
Factor
9 - 29 All