Download 4-3 Greatest Common Factor

4-3 Greatest Common Factor
Learn to find the greatest common factor
(GCF) of a set of numbers.
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4-3 Greatest
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TitleFactor
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Common
Vocabulary
greatest common factor (GCF)
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4-3 Greatest Common Factor
Factors shared by two or more whole numbers
are called common factors. The largest of the
common factors is called the greatest
common factor, or GCF.
Factors of 24:
Factors of 36:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
The greatest common factor (GCF) of 24 and 36
is 12.
Example 1 shows three different methods for
finding the GCF.
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4-3 Greatest Common Factor
Additional Example 1A: Finding the GCF
Find the GCF of each set of numbers.
A. 28 and 42
Method 1: List the factors.
factors of 28: 1, 2, 4, 7, 14, 28
List all the factors.
factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Circle the GCF.
The GCF of 28 and 42 is 14.
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4-3 Greatest Common Factor
3 Methods:
•T-Chart
•Tree
•Ladder
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4-3 Greatest Common Factor
Additional Example 1C: Finding the GCF
Find the GCF of each set of numbers.
C. 45, 18, and 27
Method 3: Use a ladder diagram.
3
45 18 27
3 15 6 9
5 2 3
3•3= 9
Begin with a factor that divides into
each number. Keep dividing until the
three have no common factors.
Find the product of the numbers
you divided by.
The GCF of 45, 18, and 27 is 9.
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4-3 Greatest Common Factor
Try This: Example 1C
Find the GCF of each set of numbers.
C. 40, 16, and 24
Method 3: Use a ladder diagram.
2
Begin with a factor that divides into
40 16 24
each number. Keep dividing until the
2 20 8 12
three have no common factors.
2 10 4 6
5 2 3
2 • 2 • 2 =8
Find the product of the numbers
you divided by.
The GCF of 40, 16, and 24 is 8.
Course 1
4-3 Greatest
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TitleFactor
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Lesson Quiz: Part 1
Find the greatest common factor of each
set of numbers.
1. 18 and 30
6
2. 20 and 35
5
3. 8, 28, 52
4
4. 44, 66, 88
22
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