Let's first find the greatest common factor of 66 and 30.
To do this, start by dividing 66 by every natural
number you can until you hit repeat factors.
Also note, we need factors that are natural numbers! No decimals!
66 ÷ 1 = 66
66 ÷ 2 = 33
66 ÷ 3 = 22
66 ÷ 6 = 11
We can stop here because if we continue dividing, we hit repeat factors.
So the factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.
Now do the same for 30.
30 ÷ 1 = 30
30 ÷ 2 = 15
30 ÷ 3 = 10
30 ÷ 5 = 6
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Now look for the largest number shared by the two lists.
In this case, we have 6 as our gcf for the numbers.
Now let's do the variables.
To qualify for the Greatest Common Factor,
the variable must appear in every monomial.
Since the y doesn't appear in every monomial, it does not qualify.
If the variable does appear in every monomial, the Greatest
Common Factor will use the smallest power on that variable.
In this case, the smallest power between x and x² is x.
So our answer is 6x.
