Greatest Common Factor
4-2
MAIN IDEA
Find the greatest common factor of two or more numbers.
Greatest Common Factor
VENN DIAGRAM The Venn diagram shows the prime factors of 12 and 18.
1. Which factors are in the
Prime Factors Prime Factors of 12 of 18
New Vocabulary
Venn diagram greatest common factor (GCF)
overlapping section? What does this mean?
2. Is the product of 2 and 3 also
Math Online glencoe.com • Extra Examples • Personal Tutor • Self-Check Quiz • Reading in the Content Area
a factor of 12 and 18?
3. Make a Venn diagram showing the prime factors of 12 and 20.
Identify the common factors and find their product. 1–3. See margin. As shown above, Venn diagrams use overlapping circles to show how 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.
List the factors of 18 and 48.
factors of 18: 1, 2, 3, 6, 9, 18 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 = 2 × 3 × 3 48 = 2 × 2 × 2 × 2 × 3
Write the prime factorizations of 18 and 48.
The greatest common factor or GCF is 2 × 3 or 6.
Find the GCF of each pair of numbers.
a. 8, 10
2
b. 6, 12
6
c. 10, 17
1
186
Chapter 4 Fractions, Decimals, and Percents
Reading Math
Greatest Common Factor The greatest common factor is also called the greatest common divisor because it is the greatest number that divides evenly into the given numbers.
Find the GCF of Three Numbers
2 Find the GCF of 12, 24, and 60.
Write the prime factorization. Circle the common prime factors. 12 = 2 × 2 × 3 24 = 2 × 2 × 2 × 3 60 = 2 × 2 × 3 × 5 The
MAIN IDEA
Find the greatest common factor of two or more numbers.
Greatest Common Factor
VENN DIAGRAM The Venn diagram shows the prime factors of 12 and 18.
1. Which factors are in the
Prime Factors Prime Factors of 12 of 18
New Vocabulary
Venn diagram greatest common factor (GCF)
overlapping section? What does this mean?
2. Is the product of 2 and 3 also
Math Online glencoe.com • Extra Examples • Personal Tutor • Self-Check Quiz • Reading in the Content Area
a factor of 12 and 18?
3. Make a Venn diagram showing the prime factors of 12 and 20.
Identify the common factors and find their product. 1–3. See margin. As shown above, Venn diagrams use overlapping circles to show how 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.
List the factors of 18 and 48.
factors of 18: 1, 2, 3, 6, 9, 18 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 = 2 × 3 × 3 48 = 2 × 2 × 2 × 2 × 3
Write the prime factorizations of 18 and 48.
The greatest common factor or GCF is 2 × 3 or 6.
Find the GCF of each pair of numbers.
a. 8, 10
2
b. 6, 12
6
c. 10, 17
1
186
Chapter 4 Fractions, Decimals, and Percents
Reading Math
Greatest Common Factor The greatest common factor is also called the greatest common divisor because it is the greatest number that divides evenly into the given numbers.
Find the GCF of Three Numbers
2 Find the GCF of 12, 24, and 60.
Write the prime factorization. Circle the common prime factors. 12 = 2 × 2 × 3 24 = 2 × 2 × 2 × 3 60 = 2 × 2 × 3 × 5 The