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Euler's Totient Function from Prime Factorisation Calculator

φ(n) = n · ∏ (1 − 1/pᵢ) over the distinct prime factors.

Compute Euler's totient φ(n) — the count of integers in 1..n coprime to n — directly from the prime factorisation. Enter up to 4 distinct primes pᵢ and their exponents aᵢ; the calculator forms n = ∏ pᵢ^aᵢ and applies φ(n) = n · ∏ (1 − 1/pᵢ). Set an exponent to 0 to skip that prime.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

φ(n) = n · ∏ (1 − 1/pᵢ).

In depth

Compute Euler's totient φ(n) — the count of integers in 1..n coprime to n — directly from the prime factorisation. Enter up to 4 distinct primes pᵢ and their exponents aᵢ; the calculator forms n = ∏ pᵢ^aᵢ and applies φ(n) = n · ∏ (1 − 1/pᵢ). Set an exponent to 0 to skip that prime.