Coprime Count Calculator
Count the positive integers up to a positive integer that are coprime to it (Euler totient).
Description
Count the positive integers up to a positive integer that are coprime to it (Euler totient).
Count the positive integers up to a positive integer that are coprime to it (Euler totient).
When to use Coprime Count Calculator
Use this tool to test or transform exact integers according to the named number-theory definition, for education, validation, or algorithm checks.
- Integer
- An integer input greater than or equal to 1.
How the calculation works
The formula below determines the tool output. Coprime count: The calculated coprime count.1
φ(n) = count of integers k in 1…n with gcd(k, n) = 1 Limitations and assumptions
This tool applies an exact integer definition within JavaScript's safe-integer range. It is not an arbitrary-precision factorization or proof system, so do not use rounded measurements or integers beyond the accepted domain as though they were exact.
Alternative or Complementary approaches
Complement a number-property result with its factorization, divisors, digit representation, or a second independent predicate. A true result establishes only the named property and does not imply other properties such as primality.
References
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Euler's totient function — Wikipedia contributors
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