Euler's Totient Calculator – Up To 20 Digits!

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Input a number n: Euler's totient function φ(n): Run time:

Euler's totient function φ(n) is the number of positive integers not exceeding n that have no common divisors with n (other than the common divisor 1).

In other words, φ(n) is the number of integers m coprime to n such that 1 ≤ mn.
(Note that the number 1 is counted as coprime to all positive integers including itself.)

SOME TEST CASES FOR EULER'S TOTIENT FUNCTION:
φ(1) = 1
φ(2) = 1
φ(20) = 8
φ(36) = 12
φ(81) = 54
φ(90) = 24
φ(100) = 40
φ(9007199254740881) = 9007199254740880
φ(9007199254740997) = 9007199254740996
φ(999999999999999999) = 441994921381739520
φ(9999999999999999999) = 6666666666666666660
φ(99999999999999999999) = 58301444908800000000

See also:
• 100+ digit calculator: arbitrary precision arithmetic
• Prime factorization calculator
• Highly composite numbers
• Divisors and sum-of-divisors calculator

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