To find the greatest common factor (GCF) of 42a^2b and 60ab^2, we first need to break down each term into its prime factors. For 42a^2b, the prime factors are 2 * 3 * 7 * a * a * b. For 60ab^2, the prime factors are 2 * 2 * 3 * 5 * a * b * b. Comparing the prime factors of both terms, we can identify the common factors: 2, 3, a, and b. Therefore, the GCF of 42a^2b and 60ab^2 is 6ab.