Chapter 4 Fractions, Decimals, And Percents - Lesson 4-2 Greatest Common Factor Worksheet

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4-2
Greatest Common Factor
MAIN IDEA
VENN DIAGRAM
The Venn
Find the greatest
Prime Factors
Prime Factors
diagram shows the prime
common factor of two
of 12
of 18
or more numbers.
factors of 12 and 18.
Which factors are in the
1.
New Vocabulary
overlapping section? What
Venn diagram
does this mean?
greatest common
factor (GCF)
Is the product of 2 and 3 also
2.
a factor of 12 and 18?
Math Online
Make a Venn diagram showing the prime factors of 12 and 20.
3.
Identify the common factors and find their product. 1–3. See margin.
• Extra Examples
• Personal Tutor
• Self-Check Quiz
As shown above, Venn diagrams use overlapping circles to show how
• Reading in the Content Area
common elements among sets of numbers or objects are related. They
can also show common factors. The greatest of the common factors of
two or more numbers is the greatest common factor, or GCF.
Find the Greatest Common Factor
1
Find the GCF of 18 and 48.
METHOD 1
List the factors of the numbers.
factors of 18: 1, 2, 3, 6, 9, 18
List the factors
of 18 and 48.
factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The common factors of 18 and 48 are 1, 2, 3, and 6.
So, the greatest common factor or GCF is 6.
METHOD 2
Use prime factorization.
Write the prime factorization. Circle the common prime factors.
18 =
× 3 ×
2
3
Write the prime factorizations
of 18 and 48.
48 =
× 2 × 2 × 2 ×
2
3
The greatest common factor or GCF is 2 × 3 or 6.
Find the GCF of each pair of numbers.
8, 10 2
6, 12 6
10, 17 1
a.
b.
c.
186
Chapter 4 Fractions, Decimals, and Percents

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