Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P2 P3P4, 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 f, and f. Then f, corresponds to a subset of {P1 P2: P3 Pa, and f, corresponds to the complement of that subset.) (c) If n = P, P2P3PaPs, 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= Pi 2 P where the p, are distinct prime numbers, how many ways can n be written as 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 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P2 P3P4, 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 f, and f. Then f, corresponds to a subset of {P1 P2: P3 Pa, and f, corresponds to the complement of that subset.) (c) If n = P, P2P3PaPs, 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= Pi 2 P where the p, are distinct prime numbers, how many ways can n be written as product of two positive integer factors?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
See similar textbooks
icon
Related questions
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 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P, P3PA 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 f, and f,. Then f, corresponds to a subset of {P1 P2. P31 P4}, and f, corresponds to the complement of that subset.) (c) If n = p, P, P3PAP5, 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 = p, P, ... Pr where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?
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 770 can be written as a product of two positive integer factors. (Enter your answer as a comma-separated list of products.) (b) If n = p, P, P3PA 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 f, and f,. Then f, corresponds to a subset of {P1 P2. P31 P4}, and f, corresponds to the complement of that subset.) (c) If n = p, P, P3PAP5, 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 = p, P, ... Pr where the p, are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 7 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Fundamental Counting Principle
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Algebra
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
SEE MORE TEXTBOOKS