Euler's Totient Function
Calculate Euler's totient function φ(n)
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 (sharing no common factors except 1). This fundamental number theory function is essential in cryptography, particularly RSA encryption, and appears frequently in mathematical proofs and algorithms. The calculator quickly determines how many numbers less than or equal to your input have no common divisors with it, making complex mathematical computations accessible for students, researchers, and cryptography applications.
How to use
Enter any positive integer n into the input field and click calculate. The calculator will compute φ(n) by finding all numbers from 1 to n that share no common factors with n except 1. The result shows the count of these relatively prime numbers, along with the mathematical steps used in the calculation.
Frequently asked questions
What does φ(n) represent in Euler's totient function?
φ(n) represents the count of positive integers less than or equal to n that are coprime to n, meaning they share no common factors except 1.
Why is Euler's totient function important in cryptography?
It's crucial for RSA encryption key generation, helping determine the public and private key pairs by calculating φ(p×q) for prime numbers p and q.
What is φ(n) for prime numbers?
For any prime number p, φ(p) = p - 1, since all numbers from 1 to p-1 are coprime to p.