QQuestionMathematics
QuestionMathematics
"Which pair of numbers is relatively prime?
A. 7 and 21
B. 4 and 15
C. 6 and 9
D. 9 and 27"
6 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1: Recall the definition of relatively prime numbers.
Two numbers are said to be relatively prime if their greatest common divisor (GCD) is 1.
Step 2: Determine the GCD for each pair of numbers.
(A) 7 and 21: \text{GCD}(21, 7) = \boxed{7} Since the GCD is not 1, these numbers are not relatively prime. (B) 4 and 15: \text{GCD}(15, 4) = \text{GCD}(4, \text{remainder of } 15 \div 4) = \text{GCD}(4, 3) = \text{GCD}(3, \text{remainder of } 4 \div 3) = \text{GCD}(3, 1) = \boxed{1} Since the GCD is 1, these numbers are relatively prime. (C) 6 and 9: \text{GCD}(9, 6) = \text{GCD}(6, \text{remainder of } 9 \div 6) = \text{GCD}(6, 3) = \text{GCD}(3, \text{remainder of } 6 \div 3) = \text{GCD}(3, 0) = \boxed{3} Since the GCD is not 1, these numbers are not relatively prime. (D) 9 and 27: \text{GCD}(27, 9) = \text{GCD}(9, \text{remainder of } 27 \div 9) = \text{GCD}(9, 0) = \boxed{9} Since the GCD is not 1, these numbers are not relatively prime.
Final Answer
The pair of numbers that are relatively prime is (B) 4 and 15.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students