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): 142, 221, 314, 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.) 1.570.2 285,3-190.5 114, 6-95,10 57,15-38.19.30 (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: Supposen can be written as a product of two positive integer factors f, 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. P where the p, are distinct 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): 142, 221, 314, 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.) 1.570.2 285,3-190.5 114, 6-95,10 57,15-38.19.30 (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: Supposen can be written as a product of two positive integer factors f, 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. P where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I need help with Part D please
Transcribed Image Text:The number 42 has the prime factorization 23. 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): 142, 221, 314, 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.)
1.570,2 285,3 190,5 114, 6-95,10-57,15-38,19-30
(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?
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