1. What Are Relatively Prime Numbers?

Two numbers are relatively prime (or coprime) if their greatest common divisor (GCD) is 1. This means they share no positive integer factors other than 1.

2. How Does the Calculator Work?

The calculator uses the Euclidean algorithm to find the GCD of two numbers:

If the GCD is 1, the numbers are relatively prime.

3. Importance of Relatively Prime Numbers

Details: Relatively prime numbers are fundamental in number theory and have applications in cryptography (like RSA algorithm), modular arithmetic, and fractions simplification.

4. Using the Calculator

Tips: Enter two positive integers. The calculator will determine if they're relatively prime and show their GCD.

5. Frequently Asked Questions (FAQ)

Q1: Are all prime numbers relatively prime to each other?
A: Yes, any two distinct prime numbers are relatively prime since their only common factor is 1.

Q2: Can a number be relatively prime to itself?
A: Only the number 1 is relatively prime to itself since gcd(1,1) = 1. All other numbers have gcd(n,n) = n ≠ 1.

Q3: What's the difference between prime and relatively prime?
A: Prime refers to a number with exactly two distinct factors (1 and itself). Relatively prime refers to a pair of numbers whose GCD is 1.

Q4: Are consecutive integers relatively prime?
A: Yes, any two consecutive integers are relatively prime (gcd(n, n+1) = 1).

Q5: How is this used in cryptography?
A: RSA encryption relies on choosing large numbers that are relatively prime to ensure security through the difficulty of factorization.