Start with the smallest number, 18:
       The factors of 18 are: 1, 2, 3, 6, 9, 18.
So the GCF for all three must be one of those.
Now consider the next smallest number.  Of the factors of 18, only these are also factors of 27:
     1, 3, 9
Now consider the last number, 54.  Of the remaining factors, 9 is the greatest and 9 goes into 54.
The GCF is 9.
By starting with the smallest number, you usually limit how many factors you'll ever need to consider.