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 798 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 district prime numbers, how many can n be written as a product of two positive integer factors? (d) If n= p1 p2 ... pk where the pi are district prime numbers, how many ways can n be written as a product of two positive integer factors?
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 798 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 district prime numbers, how many can n be written as a product of two positive integer factors?
(d) If n= p1 p2 ... pk where the pi are district prime numbers, how many ways can n be written as a product of two positive integer factors?
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