Find Greatest Common Factor

Examples, videos, worksheets, and solutions to help Grade 6 students learn how to find the greatest common factor using prime factorization and factor trees.

The following diagram shows an example of finding the greatest common factor using factor trees and prime factorization. Scroll down the page for more examples and solutions on the greatest common factor (GCF).

 

How to find the greatest common factor by using factor trees?
The greatest common factor is the biggest number that divides evenly into each number in a given set of numbers.
Find the prime factorization of a number and use that to find the greatest common factor between two or three numbers.
Examples:

1. Find the greatest common factor of 12 and 8.
2. Find the greatest common factor of 18 and 21.
3. Find the greatest common factor of 24, 32 and 40.

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Greatest common factor using prime factorization or factor trees
Example:
Find the GCF of 18, 20 and 6.

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Three examples of how to find the greatest common factor of a set of terms using the factor tree
Example:
Find the Greatest Common Factor of the following numbers.

1. 24, 36, 60
   
2. 28x², 42⁴, 49x³
   
3. 24a⁴b², 60a³b, 144a³b³

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How to find the greatest common factor (GCF) using factor trees and exponents?
Example:
Find the GCF of 60, 18 and 28.

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Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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