Reference no: EM131574018

Question: 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 210 can be written as a product of two positive integer factors.

b. If n = p1 p2 p3 p4, where the pi are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?

c. If n = p1 p2 p3 p4 p5, where the pi 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 pi are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?