The number 42 has the prime factorization 2 · 3 ·7. Thus, 42 can be written in four ways as a product of two positive integer factors (without regard to the order of the factors): 1 42,2 21,3 14, and 6 · 7. Answer a-d below without regard to the order of the factors. (a) List the distinct ways the number 570 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = P1 P2 P3 P4, where the p; are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (Hint: Suppose n can be written as a product of two positive integer factors f₁ and f₂. Then f₁ corresponds to a subset of {P1, P2, P3, P4), and f₂ corresponds to the complement of that subset.) (c) If n = P1 P2 P3 P4 P5, where the p; are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? (d) If n = P1 P2 Pk, where the p; are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?