Math Tip Of The Day: GCF Part 1

In mathematics, you sometimes have to find the GCF (greatest common factor).  This concept is used once students have learned multiplication, and is also used in Algebra when factoring polynomials.  Part 1 of this math tip will focus simply on finding the GCF of whole numbers.  Part 2 will extend to factoring polynomials.

First of all, what is a factor?  A factor is a number that is multiplied to get another number or product.  So, the factors of 2 are 1 and 2, since they are the only numbers that can multiply to arrive at a product of 2.  

Anytime that I’ve had to find the GCF, or the largest common factor of two numbers, I’ve made a T-table to assist me.  For example, if you need to find the GCF of the numbers 30 and 75, you can set up a T-table to do so.  See the diagram below.

I list the numbers that I need the GCF for at the top of the table.  Underneath each number, I list all of the factors.  For 30, I know that 1 x 30, 2 x 15, 3 x 10 and 5 x 6 all equal 30.  So I list them in pairs.  I did the same for the number 75.  Then I circle all the factors that both numbers have in common.  Once all common factors are circled, I find the largest of those numbers and place a check mark.  This indicates the GCF for those numbers.

It’s really not that difficult to find the GCF, but there are some things to keep in mind.  Look at the following tips:

  •  1 and the number itself will always be factors.  So if you can’t think of any other factors, at least you’ll have those two.
  • The number 1 will more than likely NOT be the GCF.  All numbers have a factor of 1.  The only way that 1 will be the GCF is if both numbers are prime numbers (which means they have no other factors than 1 and themselves).
  • Multiplication is key.  The better you are at multiplication, the better you will be at finding the factors of numbers.
  • When in doubt, try out every possible whole number.  Divide the number by 1, then 2, then 3 and so on until you’ve found all possible factors.
So, feeling confident that you can find the GCF?  Try these examples.
  1. 24 and 28
  2. 25 and 55
**Stay tuned for Part 2 of this Math Tip!!