   Chapter 9.5, Problem 24ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# 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 210 can be written as a product of two positive integer factors. b. If n = p 1 p 2 p 3 p 4 , where the p i are distinct prime numbers, how many ways can n be written as a product of two positive integer factors? c. If n = p 1 p 2 p 3 p 4 p 5 , where the p i are distinct prime numbers, how many ways can n he written as a product of two positive integer factors? d. If n = p 1 p 2 … p k , where the p i are distinct prime numbers, how many ways can n be written as a product of two positive integer factors?

To determine

(a)

To list the distinct ways which the number 210 can be written as a product of two positive integer factors.

Explanation

Given information:

210

Concept used:

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

Calculation:

The number 210 has the prime factorization is written in 7 ways,

This implies

210=1.210210=2.105210=3.70210=5.42210=7.30210=10

To determine

(b)

To find how many ways can n be written as a product of two positive integer factors.

To determine

(c)

To find how many ways can n be written as a product of two positive integer factors.

To determine

(d)

To find how many ways can n be written as a product of two positive integer factors.

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