In order to find the greatest common factor of two numbers you must first know the factors of each number in question. The factors are the numbers that can be divided within a particular number.

Take the number 24 for instance; the factors of 24 are as follows: 1, 2, 3, 4, 6, 8, 12, and 24. Now that we know the factors of 24, we can begin to add another number into the equation to try and find the greatest common factor of a group of numbers.

Since we already have the number 24, we can use the number 18 as the second number. The factors of 18 are as follows; 1, 2, 3, 6, 9, and 18.

Lets take a look at these two factored numbers together; GCF (18, 24) the factors side by side look like this 1, 2, 3, 4, 6, 12, 24 and 1, 2, 3, 6, 9, 18. Now that we can see these two factored out numbers together, we can find the greatest common factor by using the simplest form possible.

If we pretend that the number one is not there and multiply all the other numbers that 18 and 24 have in common we would get this: 2*3 since 2 and 3 are the only two numbers that these numbers have in common. Now we multiply these two numbers to get this; 2*3=6 which is the greatest common factor of 18 and 24. This method can be used to find the greatest common factor of any numbers but is most often used in smaller numbers.

If you have any questions or would like for me to explain a bit further, please feel free to email me or comment with your thoughts.