Euler's Totient Function Calculator
Calculate Euler's totient function φ(n) and analyze coprime relationships
About this calculator
Euler's Totient Function Calculator computes φ(n), which counts the positive integers up to n that are relatively prime to n (share no common factors except 1). This fundamental number theory function is essential in cryptography, particularly RSA encryption, and helps analyze mathematical relationships between numbers. The calculator provides instant results and detailed analysis of coprime relationships, making it valuable for students, mathematicians, and cryptography professionals studying modular arithmetic and prime number theory.
How to use
Enter any positive integer n into the input field and click calculate. The calculator will compute φ(n) using the efficient formula involving prime factorization. Results show the totient value, prime factorization of n, and detailed explanation of how the coprime count was determined.
Frequently asked questions
What does Euler's totient function φ(n) represent?
φ(n) counts how many positive integers less than or equal to n are coprime to n (share no common divisors except 1).
Why is the totient function important in cryptography?
It's crucial for RSA encryption key generation, where φ(n) helps determine valid encryption and decryption exponents for secure communication.
What is φ(p) for a prime number p?
For any prime number p, φ(p) = p-1, since all numbers from 1 to p-1 are coprime to p.