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ZingPath: Factors and Multiples

Greatest Common Factor of Numbers

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Factors and Multiples

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Lesson Focus

Greatest Common Factor of Numbers

Math Foundations

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You will find the greatest common factor of two or more numbers.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Explain the concept of greatest common factor.
  • Explain the concept of relatively prime numbers.
  • Determine the greatest common factor of two numbers.
  • Determine the greatest common factor of three or more numbers.

Everything You'll Have Covered

It is important for students to understand the value of finding the greatest common factor (GCF) for numbers because they will use the procedure regularly when finding equivalent fractions, ordering fractions with unlike denominators, and adding and subtracting fractions with unlike denominators.

The following key vocabulary terms will be used throughout this Activity Object:

Composite number - A number which has more than two factors. All composite numbers are the product of prime numbers. Composite numbers can be broken down into the prime numbers using prime factorization.


24 is a composite number.

Its factors are 1, 2, 3, 4, 6, 8, 12, and 24.

Its prime factorization is shown below:

24 = 2 2 2 3

Factor - A factor of a number will divide that number exactly, without any remainder.


2 is a factor of 16 because 2 goes into 16 exactly 8 times, with no remainder.

Greatest common factor (GCF) - The largest factor two or more numbers have in common. The GCF can be determined by listing the factors for each number or by using prime factorization.


Find the GCF of 18, 24 and 36.

Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

1, 2, 3 and 6 are common factors for 18, 24, and 36. The greatest common factor (GCF) is 6.


18 = 2 3 3

24 = 2 2 2 3

36 = 2 2 3 3

The common factors are 2 and 3. The product of the common factors 2 3 is 6. The greatest common factor is 6.

Prime factorization - A process of breaking down a composite number into the product of prime numbers.


12 = 2 2 3

Prime numbers - A number which has a factor of one and itself. (1 is neither prime nor composite.)

Tutorial Details

Approximate Time 25 Minutes
Pre-requisite Concepts Students should be familiar with factors, prime factorization, and prime numbers.
Course Math Foundations
Type of Tutorial Concept Development
Key Vocabulary multiples, prime factorization, the greatest common factor