How does the Eulers Totient Function work?

For prime p: φ(p) = p−1 Then: φ(pᵏ) = pᵏ−pᵏ⁻¹ Then: Multiplicative: φ(mn) = φ(m)φ(n) when gcd(m,n)=1 Then: φ(12) = φ(4)×φ(3) = 2×2 = 4.

Can you give an example of how to use the Eulers Totient Function?

Example: Input φ(12) gives a result of 4 (coprime: 1,5,7,11).

Is the Eulers Totient Function free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Eulers Totient Function?

Our Eulers Totient Function uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Eulers Totient Function

Euler's Totient Function φ(n)

n (positive integer ≤ 1,000,000)

φ(n) = count of integers from 1 to n that are coprime to n.

Euler's totient function φ(n) counts how many integers from 1 to n are coprime to n (share no common factor other than 1). It is fundamental in number theory and RSA encryption.

Symbol	Name	Unit	Description
n	positive integer	—	—
φ(n)	Euler totient of n	—	count of integers coprime to n

n	φ(n)	Coprime integers
6	2	1,5
10	4	1,3,7,9
12	4	1,5,7,11
20	8	1,3,7,9,11,13,17,19

References

›Euler's totient function — Wolfram MathWorld

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Eulers Totient Function

Euler's Totient Function φ(n)

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Euler Totient Values

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Euler's Totient Function φ(n)