Euler's Totient φ(n)

Count integers coprime to n

φ(n) = n · ∏ (1 − 1/p) over primes p | n

Euler's totient φ(n)

integers in 1…n coprime to n

Prime factorization

2² × 3

Euler product

12 × (1 − 1/2) × (1 − 1/3) = 4

Integers coprime to n

1, 5, 7, 11

About this calculator

Euler's Totient calculator computes φ(n), the count of integers from 1 to n that are coprime to n. See the prime factorization, the Euler product φ(n) = n·∏(1−1/p), and the coprime residues laid out on a grid.