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The Greatest Common Factor (GCF) is the largest number that can evenly divide two numbers. In other words, it is the greatest common divisor or factor that two numbers share.
There are several ways that you can find the GCF (or GCD, the Greatest Common Divisor) of two numbers.
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In elementary school, most of the time the method used to teach the concept is to list all of the factors of the numbers like this:
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Then, you'd match up those factors that both numbers share until you come to the one factor that is the largest.
The largest matching pair is the GCF.
The GCF of 24 and 36 is 12.
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A much more effective method, when dealing with larger numbers (particularly when you may not know all of the factors off the top of your head!) is to use Prime Factorization. By making a factor tree to factor out all the prime numbers and then finding what factors they have in common is a not only an easier way to find the GCF but, when dealing with larger numbers, much easier in case you don't know what all the factors are!
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Let's try it with 48 and 72. If we want to find the GCF of 48 and 72, first we make the factor trees for each.
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Then, go through each side's primes and cross off the ones they have IN COMMON. Write those down and multiply. That will give you the GCF.
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For some extra practice in finding the Greatest Common Factor between a pair of numbers, then, click GCF Practice Page
If you want even MORE practice, then click More GCF Practice.
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©2009–2010 Sherry Skipper Spurgeon. All Rights. Reserved.
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