How to Find the GCF of Numbers
The greatest common factor (GCF) of a set of numbers is the largest number that is a common factor of those numbers. A factor is a number that divides into a number evenly, without leaving a remainder. Being able to find the greatest common factor of a number is an important math skill to learn because it will come in handy when you start to learn how to factor polynomials.
Other People Are Reading
Instructions
-
Finding the GCF of Numbers
-
1
Ask yourself if there is a common factor of the numbers, or a number that divides into both numbers without leaving a remainder. If the numbers you are dealing with are small enough then you might be able to think of all the common factors of the number without having to make any lists and determine quickly the largest common factor the numbers share. For example, if your two numbers are 12 and 15 then you can make a list of each number's factors mentally. For 12 the factors are 1, 12, 3, 4, 2, and 6. For 15 the factors are 1, 15, 3, and 5. So, you can then do a quick mental comparison of the two lists and determine that 3 is the greatest common factor of 12 and 15 because that is the largest factor they have in common.
-
2
Make a list of all the factors of all the numbers in your set if you can't determine all the numbers' common factors in your head. If you couldn't do the problem in the previous Step in your head, then you would write down your list of factors for both 12 and 15.
-
-
3
Look at all your lists and make another list of numbers that appear in all of your lists. For the example in Step 1 you would write a second list of common factors--1 and 3.
-
4
Look through your new list for the largest number in the list, this will be the greatest common factor. For the example, you would choose 3 because that is the greatest common factor of 12 and 15.
-
1
Tips & Warnings
If you are dealing with 2 even numbers then 2 is going to be a common factor.
You can determine if 3 is a factor of a number by adding the digits of a number together and seeing if that number is divisible by 3. For example, if one of your numbers was 12 you would add 1+2=3 which is divisible by 3 so 3 is a factor of 12.
