This answer uses NMF, which if needed you can read the syntax on my profile:
If we do a partial prime factorisation, we get these, where a and b are the sets containing the prime factors:
a = 10•2 = 20 = {2}^{2}•5
b = 15x{y}^{2} = 3•5•x•{y}^{2}
a∩b = {5}
multiply the elements of a∩b = 5
Therefore the GCF of 10•2 and 15•x•{y}^{2} is 5
