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?

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?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

R=(C-S/t) S (Business)
DI 8. 2x3(9x2 +5y) 9. (6a+1)(5a+2) 10. -4x²y(x² +7xy-6y) 11. (x-2)(x² search
I need help with both!!!
doesn't make sense. can you please explain a bit better?
i need the answer quickly
urgent.
How can we transform non-linear equations.