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The Greatest Common Factor of Numbers

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The Greatest Common Factor of Numbers

Algebra-1

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You will learn how to 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

Finding the greatest common factor.

The greatest common factor (GCF) is the largest factor two or more numbers have in common. The GCF can be determined by listing the factors for each number.

Example:

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.

Using prime factorization to find the greatest common factor

Prime factorization is a process of breaking down a composite number into the product of prime numbers. Prime factorization can also be used to find the greatest common factor of two or more numbers.

Using the example from above,

Find the GCF of 18, 24 and 36.

18 = 2 3 3

24 = 2 2 2 3

36 = 2 2 3 3

The common prime factors are 2 and 3. The greatest common factor (GCF) is 6 (2 3).

Here is another example using large numbers:

Find the GCF of 210, 315, and 350.

210 = 2 3 5 7

315 = 3 3 5 7

350 = 2 5 5 7

The common prime factors are 5 and 7. The greatest common factor (GCF) is 35 (5 7). Although 350 has two 5's for its factors, we only use one of them because 210 and 315 only have one 5 as a factor.

Tutorial Details

Approximate Time 30 Minutes
Pre-requisite Concepts Students should know the definitions of factors, prime factorization, and prime numbers.
Course Algebra-1
Type of Tutorial Concept Development
Key Vocabulary greatest common factor, factor, prime factorization