The greatest common factor is 2 u^3 v^4
In order to find this, you have to determine the highest number that will go in evenly to both of the leading coefficients. The factors of 6 are 1, 2, 3, and 6. Both 3 and 6 don't go evenly into 44, so 2 is the greatest factor.
Then you just take the highest number of u's that are in both. There are 6 in the first term and 3 in the second. So, you can take 3 from both.
Then you do the same thing for v's. There are 4 in the first term and 5 in the second term. So, 4 is the highest number we can take from both.