Which of the following numbers are coprime?

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Understanding Coprime Numbers

Coprime numbers, also known as relatively prime numbers, are pairs of numbers that share no common factors other than 1. This means their greatest common divisor (GCD) is 1. Let’s explore how to determine if a set of numbers is coprime.

Identifying Coprime Numbers

To find if given numbers are coprime, follow these steps:

  1. List the Numbers: Take the numbers you want to check. For example, let’s say we have the numbers 8, 15, and 27.
  2. Find the GCD: Calculate the greatest common divisor for each pair of numbers.
  3. Evaluate the Results: If the GCD of any pair is 1, those numbers are coprime.

Example

Consider the numbers 8, 15, and 27:

  • GCD(8, 15) = 1
  • GCD(8, 27) = 1
  • GCD(15, 27) = 3

In this case, 8 and 15 are coprime, and 8 and 27 are also coprime. However, 15 and 27 share a common factor of 3, meaning they are not coprime.

Conclusion

To summarize, two numbers are coprime if their only common divisor is 1. Understanding coprimality is crucial in various mathematical concepts and applications, such as number theory and simplifying fractions.

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