Difficulty: Medium
Average Score: 70%
Practice
Relatively prime numbers share no common factors other than 1. Which of the following pairs of numbers are relatively prime?
Correct answer
B
Rationale
Rationale:
- Relatively prime numbers are numbers that share no common factors other than 1.
- To determine if two numbers are relatively prime, we need to find the greatest common divisor (GCD) of the two numbers. If the GCD is 1, then the numbers are relatively prime.
- Let's calculate the GCD for each pair of numbers:
A) GCD(12, 16) = 4, not relatively prime
B) GCD(15, 17) = 1, relatively prime
C) GCD(20, 24) = 4, not relatively prime
D) GCD(28, 36) = 4, not relatively prime
Therefore, the pair of numbers 15 and 17 are relatively prime because their greatest common divisor is 1, meaning they share no common factors other than 1.
- Relatively prime numbers are numbers that share no common factors other than 1.
- To determine if two numbers are relatively prime, we need to find the greatest common divisor (GCD) of the two numbers. If the GCD is 1, then the numbers are relatively prime.
- Let's calculate the GCD for each pair of numbers:
A) GCD(12, 16) = 4, not relatively prime
B) GCD(15, 17) = 1, relatively prime
C) GCD(20, 24) = 4, not relatively prime
D) GCD(28, 36) = 4, not relatively prime
Therefore, the pair of numbers 15 and 17 are relatively prime because their greatest common divisor is 1, meaning they share no common factors other than 1.