Greatest Common Factor with Variables

In this section, we will learn how to find the Greatest Common Factor with Variables. Essentially, we are learning how to find the Greatest Common Factor for a Group of Monomials. Previously, we learned that the GCF or greatest common factor is the largest number that each number of a group is divisible by. Also, recall that the GCF is also known as the GCD or greatest common divisor. These terms are interchangeable and mean exactly the same thing. To find the GCF for a group of terms, we split the operation into finding the number part and finding the variable part. We begin with the number part: factor the numbers, list every prime factor that is common to all numbers of the group. When a factor is common to all, we list the least number of times it appears in any of the factorizations. Lastly, we multiply the numbers of the list to form the number part of the GCF. For the variable part, we simply need to make sure each term has that variable. We then go with the smallest exponent that appears on any term.