Greatest Common Factors

We learned how to find the Greatest Common Factor [GCF(a,b)] of a given set of number and also the different methods we can use to find them. Maybe one of them will help you out. They are :

           -Listing Factors

           -Linear(Cuisinaire Rods)

           -Prime Factorization

When listing factors it is easiest to use the curtain method to list out your factors. When using the curtain method you list the factors from outside to inside like shown below. It is highlighted in purple.

The next step you circle the like factors & identify the largest common factor.

Therefore the GCF(18,56)=2

The Linear also known as the Cuisenaire Method is where you use small block units that are called cars and create trains with them they are each different sizes and colors and each are assigned a number.

http://www.mathcats.com/mathtoolbox/index.html

When presented with a problem like find the GCF(5,10), you can take a orange(10) car and line it up with a yellow(5) car and continue lining them up side by side until they even out and in this case 2 yellow cars even out with 1 orange car .

Prime Factorization is where we use the factors of a number to find the greatest common factor.

I find it easiest to draw out a factor tree first and find the factors that way.

     42                                      30
    /   \                                      /  \
  2    21                                   2  15
        /  \                                        /\
       3   7                                     3  5

After doing the factor tree we can hilight the end factors. after writing out that the factors of 30= 2*3*5 and the factors of 42=2*3*7. When lined up with each you find the matching numbers like for instince in this problem  2 and 3 are the only two that match up with each other so you multiply the 2 and the 3 which equals to 6. The end result will be the Greatest Common Factor of the numbers and in this problem the GCF is 6.

30= 2 * 3 * 5

42= 2 * 3 *   7

       2 * 3       =6

GCF(30,42)=6

I hope one of these methods make it easier for you to find the Greatest Common Factors.