Finding a GCF
We will now present an example of finding the GCF of two algebraic terms:
First, determine the numeric coefficient of each term:
Using the method shown earlier, find the GCF of each coefficient:
Now find the smallest exponent of each variable. For the variable j we have an exponent of 2 and an exponent of 1 (recall that a variable has an exponent of 1 if the exponent isn't explicitly shown). Thus, the lowest exponent for j is 1. So far we have
j1 or j
Now recall that in a term where a given variable is not present, the variable has an exponent of 0. Thus for the variable k we have k3 and k0. As a result, we now have
jk0 or simply j
Thus, the GCF of the variables from each term is j.
Now the GCF of the two terms is the GCF of the coefficients times the GCF of the variables. So simply write the GCF of the coefficients (numbers) with the GCF of the letters
Often, you will need to find the GCF of three or more terms. The methods are an extension of the methods presented for two terms. Instead of finding the greatest numeric factor common among two terms, you find the greatest factor that is common among the 3 or more terms. And instead of finding the lowest exponent of a given variable between two terms, find the lowest exponent of a given variable among the three or more terms.
The work for finding the GCF of three terms is shown below.