What's the trick to finding the Greatest Common Factor?

Question

Somebody told me there was a trick to finding the GCF, greatest common factor, but they didn't know what it was. So is there a trick and if so, what is it? If not, can somebody direct me to a website that might help me.

Answer 1

The Greatest Common Factor is simply the factor between two or more numbers that is the greatest. This might still be confusing, so let's try an example:

What is the greatest common factor between 12 and 18?
First, we factor them both. Make a list of all the numbers that divide evenly into them both.
Factors of 12 are 1,2,3,4,6,12. All of these numbers divide into 12 evenly.
Factors of 18 are 1,2,3,6,9,18.

Now, let's pick out the common factors (the factors that they both share): 1,2,3,6.

And the greatest of the four? 6.

There's how you do it! Let me know if you have any further questions.

Answer 2

The only way I've ever learned is to do a GCF is to list out the factors of both numbers, then the greatest of those is the GCF

For example, 24 and 36

24: 1, 2, 3, 4, 6, 8, 12, 24

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

The GCF is 12

Answer 3

One way is the Euclidean Algorithm. Here is a demo:

GCF of 25 and 60:

60/25 = 2 remainder 10
25/10 = 2 remainder 5
10/5 = 2 remainder 0

Conclusion: the GCF of 25 and 60 is 5

Method:

Start by dividing the larger number by the smaller. If it divides without remainder, the smaller number is the GCF. Otherwise, divide the number just used as divisor by the remainder you just obtained, and so on. Continue until you get a result with no remainder. When that happens, the divisor you just used to produce that "no remainder" result is the GCF.