• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q15E

Expert-verified
Discrete Mathematics and its Applications
Found in: Page 272
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

Which positive integers less than 30 are relatively prime to 30?

1, 7, 11, 13, 17, 19, 23, 29

See the step by step solution

Step by Step Solution

Step 1

The integers a and b are relatively prime, if their greatest common divisor is 1.

Let us determine the greatest common divisor of 30 and every integer less than 30.

gcd(30,1)=1gcd(30,2)=2gcd(30,3)=3gcd(30,4)=4gcd(30,5)=5gcd(30,6)=6gcd(30,7)=7gcd(30,8)=8gcd(30,9)=9gcd(30,10)=10gcd(30,11)=1gcd(30,12)=6gcd(30,13)=1gcd(30,14)=2gcd(30,15)=5gcd(30,16)=2gcd(30,17)=1gcd(30,18)=6gcd(30,19)=1gcd(30,20)=10

Step 2

gcd(30,21)=3gcd(30,22)=2gcd(30,23)=1gcd(30,24)=6gcd(30,25)=5gcd(30,26)=2gcd(30,27)=3gcd(30,28)=2gcd(30,29)=1

The positive integers less than 30 that are relatively prime to 30 are then all integers a for which gcd=30, 1=1.

a=1, 7, 11, 13, 17, 19, 23, 29

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.