Greatest Common Factor
Using Factor Trees
Jen Kershaw
Catherine Kwok
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Printed: April 14, 2016
AUTHORS
Jen Kershaw
Catherine Kwok
www.ck12.org
C HAPTER
Chapter 1. Greatest Common Factor Using Factor Trees
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Greatest Common Factor
Using Factor Trees
In this concept, you will learn to find the greatest common factor using factor trees.
Richard is making gift bags. He has 36 pencils and 28 pens. How many gift bags can Richard make if there are the
same number of pencils and pens in each bag? Use factor trees to solve this problem. How many pencils and pens
will be in each bag?
In this concept, you will learn to find the greatest common factor using factor trees.
Finding the Greatest Common Factor Using Factor Trees
The greatest common factor (GCF) is the greatest factor that two or more numbers have in common. The GCF can
be found by making a list and comparing all the factors. A factor tree can also be used to find the GCF. The GCF is
the product of the common prime factors.
Let’s find the GCF of 20 and 30 using a factor tree.
First, make a factor tree for each number.
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Then, identify the common factors. The numbers 20 and 30 have the factors 2 and 5 in common.
20 = 2 × 2 × 5
30 = 2 × 3 × 5
Next, multiply the common factors to find the GCF. If there is only one common factor, there is no need to multiply.
2 × 5 = 10
The GCF of 20 and 30 is 10.
Note that if the numbers being compared have no factors in common using a factor tree, they still have the factor 1
in common.
Examples
Example 1
Earlier, you were given a problem about Richard who needs to make gift bags with 36 pencils and 28 pens. Use
factor trees to find the most number of bags he can make that have the same number of pencils and pens in each.
First, make a factor tree for each number.
Then, identify the common factors. The common factors are two 2s.
36 = 2 × 2 × 3 × 3
28 = 2 × 2 × 7
Next, multiply to common factors to find the GCF.
2×2 = 4
Finally, divide the number of pencils and pens by the GCF, 4.
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Chapter 1. Greatest Common Factor Using Factor Trees
pencils = 36 ÷ 4 = 9
pens = 28 ÷ 4 = 7
Richard can make 4 gift bags that have 9 pencils and 7 pens in each bag.
Example 2
Find the GCF of 36 and 54 using factor trees.
First, make a factor tree for each number.
Then, identify the common factors. The numbers 36 and 54 have the factors 2 and two 3s in common.
36 = 2 × 2 × 3 × 3
54 = 2 × 3 × 3 × 3
Next, multiply the common factors to find the GCF.
2 × 3 × 3 = 18
The GCF of 36 and 54 is 18.
Example 3
Find the greatest common factor using factor trees.
14 and 28
First, make a factor tree for each number.
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Then, identify the common factors. The numbers 14 and 28 have the factors 2 and 7 in common.
14 = 2 × 7
28 = 2 × 2 × 7
Next, multiply the common factors to find the GCF.
2 × 7 = 14
The GCF of 14 and 28 is 14.
Example 4
Find the greatest common factor using factor trees.
24 and 34
First, make a factor tree for each number.
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Chapter 1. Greatest Common Factor Using Factor Trees
Then, identify the common factors. The numbers 24 and 34 have the factor 2 in common.
24 = 2 × 2 × 2 × 3
34 = 2 × 17
The GCF of 12 and 24 is 12.
Example 5
Find the greatest common factor using factor trees.
19 and 63
First, make a factor tree for each number.
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Then, identify the common factors. The numbers 19 and 63 have the factor 1 in common.
19 = 1 × 19
63 = 3 × 3 × 7
The GCF of 19 and 63 is 1.
Review
Find greatest common factor for each pair of numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
14 and 28
14 and 30
16 and 36
24 and 60
72 and 108
18 and 81
80 and 200
99 and 33
27 and 117
63 and 126
89 and 178
90 and 300
56 and 104
63 and 105
72 and 128
Review (Answers)
To see the Review answers, open this PDF file and look for section 5.6.
Resources
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/162149
MEDIA
Click image to the left or use the URL below.
URL: https://www.ck12.org/flx/render/embeddedobject/162151
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