Euler's Totient Calculator

About this calculator

This calculator finds Euler's totient φ(n) — the count of positive integers from 1 to n that are coprime with n (share no common factor with n other than 1). It's computed from n's prime factorization using the product formula φ(n) = n·∏(1 − 1/p) over each distinct prime factor p of n; for a prime p itself, φ(p) = p − 1.

The totient function is central to number theory and is the mathematical foundation of the RSA public-key cryptosystem, where φ(n) (computed from two large secret primes) is used to derive the private key from the public key. It also governs Euler's theorem, a generalization of Fermat's little theorem used throughout modular arithmetic. Enter a positive integer to get its totient value.