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 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? and 2° Then f₁ corresponds to a subset of {P1, P2, P3, P4), and f₂ corresponds to
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 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? and 2° Then f₁ corresponds to a subset of {P1, P2, P3, P4), and f₂ corresponds to
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image 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 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
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?
and
2°
Then f₁ corresponds to a subset of {P1, P2, P3, P4), and f₂ corresponds to
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