|The factors of $\,27\,$ are:||$\,1\,$||$\,3\,$||$\,9\,$||$\,27$|
|The factors of $\,18\,$ are:||$\,1\,$||$\,2\,$||$\,3\,$||$\,6\,$||$\,9\,$||$\,18\,$|
The common factors of $\,27\,$ and $\,18\,$
(the numbers that appear in both lists)
are $\,1\,$, $\,3\,$, and $\,9\,$.
The greatest common factor (the greatest number in the list of common factors) is $\,9\,$.
Here's an efficient algorithm for finding the greatest common factor,
when there aren't too many numbers, and they aren't too big.
The process is illustrated by finding the greatest common factor of $\,18\,$, $\,36\,$, and $\,90\,$:
Think about why this method works.
As you walk through each step of this discussion, keep comparing with the chart above.
Look at the prime factorizations of each number:
Here are some other ways the algorithm might be applied.
Of course, you get the same answer any correct way that you do it!
You can also zip over to wolframalpha.com and type in:
The ‘gcd’ stands for greatest common divisor, which is another name for greatest common factor.