The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 1.11: FINDING THE GREATEST COMMON FACTOR

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The greatest common factor (GCF) is the greatest factor that two (or more) numbers have in

common. To find the GCF of two numbers, follow the steps below:

1. Use exponents to write the prime factorization of each number.


2. Find the prime numbers that are factors of both numbers.


3. Choose the smaller exponent of each common prime factor. The base with the smaller
   exponent is always a factor of the same base with a larger exponent.


4. The product of the common factors is the GCF.

EXAMPLE

Find the GCF of 72 and 60.

72 = 23 × 32 60 = 22 × 3 × 5

Common factors are 2 and 3.

2 is the smaller exponent of 2. ( 22 is a factor of 23 .)

1 is the smaller exponent of 3. ( 31 is a factor of^32 .)

The GCF of 72 and 60 = 22 × 3 = 12.

DIRECTIONS: Find the GCF of each pair of numbers.

1. 9and12 2. 25 and 35 3. 6and60


2. 36 and 192 5. 36 and 30 6. 90 and 400


3. 135 and 50 8. 100 and 140 9. 45 and 200


4. 67 and 9 11. 48 and 50 12. 9and72

CHALLENGE:Do you agree with the following statement? If the GCF of two

numbers is 1, then both numbers must be prime. Explain your answer.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.