Until you get good at finding greatest common factors (GCF's), it can help to factor each term into prime factors:
90a^2b^2 = 2 * 3 * 3 * 5 * a * a * b * b
30a^2b^3 = 2 * 3 * 5 * a * a * b * b * b
40a^3b^3 = 2 * 2 * 2 * 5 * a * a * a * b * b * b
Note how I used spacing to align the common factors into columns. The GCF of these three terms will be the product of all the factors that common to all three terms. In this case, since there is one 2, one 5, two a's and two b's in each list of factors:
GCF = 2 * 5 * a * a * b * b = 10a^2b^2
And when we factor out the GCF from each term, we can look at the list of factors for each term to see "what's left":