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,...

Extracted text: 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 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P, P3PA 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 f, and f,. Then f, corresponds to a subset of {P1 P2. P31 P4}, and f, corresponds to the complement of that subset.) (c) If n = p, P, P3PAP5, 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 = p, P, ... Pr where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?