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Which positive integers less than 12 are relatively prime

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

Solution for problem 14E 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 14E

Which positive integers less than 12 are relatively prime to 12?

Step-by-Step Solution:
Step 1 of 3

Solution:Step1To findWe have to find positive integers less than 12 are relatively prime to 12Step2A Prime Number can be divided uniformly only by 1, or itself. And it must be an entire number greater than 1. Relatively prime:-Two integers x and y are said to be relatively prime if the only positive integer that divides both of them is 1. For the relatively prime to 12 we have to find greatest common divisor(gcd) for all number which is less than 12 means 1,2,3,4,5,6,7,8,9,10,11.Nowgcd(1,12)=1gcd(2,12)gcd(3,12)gcd(4,12)gcd(5,12)=1gcd(6,12)gcd(7,12)=1gcd(8,12)=4gcd(9,12)=3gcd(10,12)=2gcd(11,12)=1Therefore, 1,5,7,11 are positive integers less than 12 are relatively prime to 12.

Step 2 of 3

Chapter 4.3, Problem 14E is Solved
Step 3 of 3

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

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Which positive integers less than 12 are relatively prime