Euler Totient Calculator

Solve φ(n) = n · Π(1 − 1/p) step by step — free euler totient calculator with worked examples, real-world defaults and instant answers.

φ(n) = n · Π(1 − 1/p)

Number n

φ(36) — integers in 1..36 coprime to 36

1
Prime factorize:
36 = 2^2 × 3^2
2
Knock out each prime's share with the factor (1 − 1/p):
φ(36) = 36 × (1 − 1/2) × (1 − 1/3)
3
Compute:
φ(36) = 36 × 1/2 × 2/3 = 12

φ(n) counts how many numbers below n share no factor with it — for a prime p it's simply p − 1. Euler's theorem (a^φ(n) ≡ 1 mod n) generalizes Fermat's little theorem and is the algebraic key that makes RSA decryption undo encryption.

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Euler's totient φ(n) — count of coprimes via the product formula.

About Euler Totient Calculator

The Euler Totient Calculator solves φ(n) = n · Π(1 − 1/p) for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. φ(n) counts how many numbers below n share no factor with it — for a prime p it's simply p − 1.

How to use Euler Totient Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into φ(n) = n · Π(1 − 1/p) and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Euler Totient Calculator?

✓Solves φ(n) = n · Π(1 − 1/p) instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Euler Totient Calculator use?+

It uses φ(n) = n · Π(1 − 1/p). The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Euler Totient Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Euler Totient Calculator on your website

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