Greatest Common Factor

Greatest Common Factor: Learn

The Greatest Common Factor (GCF) is the largest number that is a factor of the target numbers.

For example, 9 is the GCF of 18 and 27 because 9 is the largest factor of both numbers.

How to find the greatest common factor:

  • Determine if there is a common factor of the numbers. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.
  • Divide all of the numbers by this common factor.
  • Repeat this process with the resulting numbers until there are no more common factors.
  • Multiply all of the common factors together to find the Greatest Common Factor

Using this process on the example above, we can find the GCF of 18 and 27.

First, we need to look for a common factor. It might be helpful to start with small numbers whose divisibility rules are easy. Unfortunately, 2 does not work because 27 is not an even number. But 3 does work, because 18÷3=6 and 27÷3=9.

Now we look at 6 and 9 (the results from dividing the 3), and we notice that again we can divide by three because 6÷3=2 and 9÷3=3.

However, now we stop because 2 and 3 do not have any common factors.

In the previous steps we were able to divide by 3 and then 3 again, so now we multiply them together (3*3) to get our Greatest Common Factor (GCF) of 9.

If the numbers have no common factors, then we can say 1 is the their GCF. In this case you could also call the numbers "relatively prime" because they have no factors in relation to each other.

GCF: Practice

What is the GCF of the two numbers?


The GCF of and is:

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