What is the gcf of 72x{^2}y and 18xy

Answer is 18xy
When finding a GCF, you need to look at  each terms separately
Let's start with coefficients.
So the factors of 18 are : 1, 2, 3, 6, 18
Which means we can only pick from these 5 when fining similarities in 72.  Well, 18 goes into 72  four  times and it is the biggest common factor.
Now we move to our variables.
If you notice, both terms have an x and y. The x^2y part just means it has 2 x's instead of one. Which means both groups have a common factor of xy.
So adding it together, you get 18xy