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Find the smallest positive integer with exactly n

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 46E Chapter 4.3

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 46E

Find the smallest positive integer with exactly n different positive factors when n is

a) 3.

b) 4.

c) 5.

d) 6.

e) 10.

Step-by-Step Solution:

Step 1 :

In this problem we have to find the smallest positive integer with n different positive factor.

Given the n values 3,4,5,6,10.

Given that ,

1 contain only one factor,

2 and 3 contain only 2 factor,

Thus 4 contain 3 factor such  has 1,2 and 4.

Hence ,

The smallest positive integer with factor 3 is 4.

Step 2 ;

      (b) Given that n=4

Number 5 contain only 2 factor

So 6 contain 4 factor such has 1,2,3,6.

Hence ,

The smallest positive integer with factor 4 is 6.

Step 3 :

      © Given that n=5

Since the number 16 contain 5 factor such has 1,2,4,8 and 16.

Hence ,

The smallest positive integer with factor 5 is 16.

Step 4 of 5

Chapter 4.3, Problem 46E is Solved
Step 5 of 5

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Find the smallest positive integer with exactly n

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