6th Grade Math Textbook, Fundamentals

5-2

Greatest Common Factor

Objective To find the greatest common factor (GCF) of two or more numbers

• To simplify fractions by using the GCF and factoring •To form equivalent fractions

Students are planting 18 forsythia and 24 lilac bushes

around the school in groups of equal number. Each group

must have the same type of bush. What is the greatest

number of bushes the students can plant in each group?

To find the greatest number of equal groupings, find

the greatest common factor of 18 and 24.

The of two or more

numbers is the greatest number that is a factor of each

of those numbers.

Here are two ways to find the GCF of two numbers:

greatest common factor (GCF)

Find the GCF of 27, 36, and 63.

Method 1 List the Factors

• List all the factors of each number.
  Factors of 27: 1, 3, 9, 27
  Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  Factors of 63: 1, 3, 7, 9, 21, 63


• Find the common factors of 27, 36, and 63.
  1, 3, 9


• Choose the greatest common factor.

The GCF of 27, 36, and 63 is 9.

1

Method 1 List the Factors

• List all the factors of each number.
  Factors of 18: 1, 2, 3, 6, 9, 18
  Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24


• List all the common factors—factors
  that are the same for both numbers.
  1, 2, 3, 6


• Choose the greatest common factor.

The GCF of 18 and 24 is 6.

Method 2 Use Prime Factorization

• Write the prime factorization of each number.


• Multiply the common prime factors.
  2 • 3 6

The GCF of 18 and 24 is 6.

Method 2 Use Prime Factorization

• Find the prime factors of each number.
  27 3 • 3• 3
  36 2 • 2 • 3• 3
  63 3 • 3• 7


• Find the common prime factors.
  3 • 3or 3^2


• 
  

  Multiply the common prime factors.
  3 • 3 9
  The GCF of 27, 36, and 63 is 9.

  
  

••

2

18

3

9

23

•••

24

22

4

3

6

2

So the students can plant 6 bushes in each group.

 &KDSWHU