Euler Totient Calculator

Summary

Enter any positive integer and get phi(n) — the count of integers from 1 to n that share no common factor with n — with a full factorization breakdown.

How it works

1. Enter a positive integer n in the input field.
2. The calculator finds the prime factorization of n.
3. phi(n) is computed using the product formula: n * product of (1 - 1/p) for each distinct prime p dividing n.
4. The step-by-step breakdown shows each prime factor and its contribution.
5. For n up to 200, the list of all coprime integers is also displayed.

Use cases

• Verify RSA key generation steps that depend on phi(n).
• Explore number theory problems involving Euler's theorem.
• Check results for cryptography and discrete math coursework.
• Find how many integers below n are coprime with n for any modulus.
• Understand primitive roots by knowing the order of the multiplicative group.
• Confirm that phi(p) = p - 1 for prime p.

Frequently Asked Questions