wikiHow to Find the Greatest Common Factor

Two Methods:Comparing Common FactorsUsing Prime Numbers

Finding the greatest common factor (GCF) of a set amount of numbers can be easy, but you'll need to know how to do it. In order to find the greatest common factor of two numbers, you're going to need to know how to factor out both of those numbers. In order to do that, you're going to need to know your timetables.

Method 1
Comparing Common Factors

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    Find factors of the number. You don't have to know prime factorization to find the greatest common factor. Start by finding all the factors of the set you are comparing.
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    Compare the sets of factors until you find the biggest number that's in both sets.

Method 2
Using Prime Numbers

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    Factor each number completely into its prime numbers. A prime number is number greater than 1 that has no factors but itself. Examples of prime numbers include 5, 17, 97, and 331, to name just a few.
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    Identify any common prime factors. Pick out any prime numbers between the set that are the same. There can be several common factors.
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    Calculate: If there's only one prime common factor, then that's your common factor. If there are multiple prime common factors, then multiply all the prime common factors together to get your greatest common factor.
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    To demonstrate this method, study this example.

Tips

  • A prime number is a number that can only be divided by one and itself.
  • Did you know that the mathematician Euclid of the third century B.C.E. created an algorithm for finding out what the greatest common factor is in the case of two natural numbers or two polynomials?

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