Euler Totient Calculator
Enter a positive integer n to calculate Euler’s totient, list its distinct prime factors, and verify the divisor count relationship.
A QUICK WALKTHROUGH
How to use this tool
- Enter a positive integer n with at most 18 decimal digits.
- Choose Calculate.
- Read φ(n), distinct prime factors, and verification values.
Definition and domain
φ(n) counts integers k with 1≤k≤n and gcd(k,n)=1. This tool accepts 1≤n≤10¹⁸ as an exact integer. JavaScript BigInt is used for the arithmetic; decimal input only, no fractions or signs.
Verification
The result is computed from the distinct prime factors p of n: φ(n)=n∏(1−1/p). The page also reports the factorization and verifies that the listed factors divide n and that the result is an integer. It does not enumerate all coprime values.
GOOD TO KNOW
Common questions
What is φ(1)?
φ(1)=1 because 1 is coprime to itself.
Are large decimals exact?
Yes, within the 18-digit input limit, using BigInt rather than floating point.
Does the tool list every coprime integer?
No. It returns the count and factorization.