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Objective
Find the greatest common factor 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
Review
Vocabulary
Factor
Two or more numbers that are multiplied
together to form a product
Review
Vocabulary
Prime number
A whole number that has exactly two factors, 1
and the number itself
Example 1 Find the GCF by Listing Factors
Example 2 Find the GCF by Using Prime Factors
Example 3 Use the GCF to Solve a Problem
1/3
Find the GCF of 36 and 48
36
48
To find the Greatest
Common Factor (GCF)
You must prime factor the
numbers
Write the numbers
Put an upside down division
sign with the numbers
1/3
Find the GCF of 36 and 48
Prime factor 36
2 36
18
36 is an even number and
the prime number 2 always
goes into an even number
Place 2 outside the house
Divide 36 by 2
Put 18 below 36
Ask “is 18 a prime number?”
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Find the GCF of 36 and 48
Ask “is 18 a prime number?”
2 36
2 18
9
2 will go into 18 evenly
Put the prime factor bar on
18
Place 2 outside the bar
Divide 18 by 2
Place 9 under 18
Ask “is 9 a prime number?”
1/3
Find the GCF of 36 and 48
Ask “is 9 a prime number?”
2 36
2 18
3 will go into 9 evenly and 3
is a prime number
3 9
3
Put the prime factor bar on 9
Place 3 outside the bar
Divide 9 by 3
Place 3 under 9
1/3
Find the GCF of 36 and 48
Ask “is 3 a prime number?”
2 36
2 18
3 9
3
2 48
3 is a prime number so you
are done prime factoring 36
Now prime factor 48
Ask “is 48 a prime number?”
2 will go into 48 because it is
even
Place 2 outside the bar
1/3
Find the GCF of 36 and 48
Divide 48 by 2
2 36
2 18
3 9
3
2 48
Place 24 under 48
2 24
Ask “is 24 a prime number?”
2 will go into 24 because it is
even
Put the prime factor bar on
24
Place 2 outside the bar
1/3
Find the GCF of 36 and 48
Divide 24 by 2
2 36
2 18
3 9
3
2 48
Place 12 under 24
2 24
2 12
Ask “is 12 a prime number?”
2 will go into 12 because it is
even
Put the prime factor bar on
12
Place 2 outside the bar
1/3
Find the GCF of 36 and 48
Divide 12 by 2
2 36
2 18
3 9
3
2 48
Place 6 under 12
2 24
2 12
2 6
Ask “is 6 a prime number?”
2 will go into 6 because it is
even
Put the prime factor bar on 6
Place 2 outside the bar
1/3
Find the GCF of 36 and 48
Divide 6 by 2
2 36
2 18
3 9
3
2 48
Place 3 under 6
2 24
2 12
2 6
3
Ask “is 3 a prime number?”
3 is a prime number so you
are done prime factoring 48
Circle factors that are common in each number and
write as factors
223
There are no more common
factors
1/3
Find the GCF of 36 and 48
2 36
2 18
3 9
3
2 48
2 24
2 12
2 6
3
Multiply the common factors
Identify the product as GCF
223
Answer: 12 = GCF
1/3
Find the GCF of 45 and 75
Answer: 15 = GCF
1/3
Find the GCF of 52 and 78
Prime factor both 52 and 78
2 52
2 26
13
2 78
3 39
13
Circle factors that are common in each number and
write as factors
2  13
Answer: 26 = GCF
Multiply the common factors
Identify the product as GCF
2/3
Find the GCF of 64 and 80 by using prime factors.
Answer: 16 = GCF
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SALES Annessa sold bags of cookies at a bake sale.
She sold small, medium, and large bags, with a
different number of cookies in each size bag. By the
end of the sale, she used 18 cookies to fill the small
bags, 27 cookies to fill the medium bags, and 45
cookies to fill the large bags. She sold the same
number of bags for the three sizes. What is the
greatest number of bags that she could have sold?
Find the factors of 18, 27, and 45
3/3
2 18
3 9
3
3 27
3 9
3
5 45
3 9
3
Circle factors that are common in each number and
write as factors
3  3
9 = GCF
Multiply the common factors
Identify the product as GCF
Answer: The greatest number of bags she could have
sold is 9 of each size
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*
CANDY Sarah is making bags of candy for a school
fund-raiser. She is making three different sizes of bags.
By the time Sarah had finished making the bags, she
had used 24 lollipops to fill the small bags, 40 lollipops
to fill the medium bags, and 64 lollipops to fill the large
bags. She completed the same number of bags for the
three sizes. What is the greatest number of bags she
could have made?
Answer: 24 bags
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Assignment
Lesson 5:1 Greatest Common Factor
10 - 24 All