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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