Euler’s Totient Function Calculator

The Euler’s Totient Function Calculator is a free online tool for calculating the value of Euler’s Totient function.

Euler's Totient Function Calculator

φ(n) = ?

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What is Euler's Totient function?

Euler’s totient function counts the positive integers up to a given integer n that are relatively prime to n. Indicated by φ(n). Relatively prime means the greatest common divisor of two integers is 1. The formula of Euler’s totient function is

The formula of Euler's totient function Where p represents all prime factors.

For example, What is the value of φ(12)?

Method 1: Calculate by normal

We know that the positive integers less than 12 are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. Among them, {1, 5, 7, 11} are relatively prime to 12. So, φ(12) = 4.

Method 2: Calculate by formula

With the prime factorization calculator, we can obtain the prime factorization of 12 is

12 = 2² * 3

So, the prime factors of 12 are 2 and 3. Put 2 and 3 into the formula

φ(12) = 12 * (1 – 12) * (1 – 13) = 12 * 12 * 23 = 6 * 23 = 4

Euler’s Totient function values corresponding to the first 100 positive integers

φ(1) = 1	φ(2) = 1	φ(3) = 2	φ(4) = 2	φ(5) = 4
φ(6) = 2	φ(7) = 6	φ(8) = 4	φ(9) = 6	φ(10) = 4
φ(11) = 10	φ(12) = 4	φ(13) = 12	φ(14) = 6	φ(15) = 8
φ(16) = 8	φ(17) = 16	φ(18) = 6	φ(19) = 18	φ(20) = 8
φ(21) = 12	φ(22) = 10	φ(23) = 22	φ(24) = 8	φ(25) = 20
φ(26) = 12	φ(27) = 18	φ(28) = 12	φ(29) = 28	φ(30) = 8
φ(31) = 30	φ(32) = 16	φ(33) = 20	φ(34) = 16	φ(35) = 24
φ(36) = 12	φ(37) = 36	φ(38) = 18	φ(39) = 24	φ(40) = 16
φ(41) = 40	φ(42) = 12	φ(43) = 42	φ(44) = 20	φ(45) = 24
φ(46) = 22	φ(47) = 46	φ(48) = 16	φ(49) = 42	φ(50) = 20
φ(51) = 32	φ(52) = 24	φ(53) = 52	φ(54) = 18	φ(55) = 40
φ(56) = 24	φ(57) = 36	φ(58) = 28	φ(59) = 58	φ(60) = 16
φ(61) = 60	φ(62) = 30	φ(63) = 36	φ(64) = 32	φ(65) = 48
φ(66) = 20	φ(67) = 66	φ(68) = 32	φ(69) = 44	φ(70) = 24
φ(71) = 70	φ(72) = 24	φ(73) = 72	φ(74) = 36	φ(75) = 40
φ(76) = 36	φ(77) = 60	φ(78) = 24	φ(79) = 78	φ(80) = 32
φ(81) = 54	φ(82) = 40	φ(83) = 82	φ(84) = 24	φ(85) = 64
φ(86) = 42	φ(87) = 56	φ(88) = 40	φ(89) = 88	φ(90) = 24
φ(91) = 72	φ(92) = 44	φ(93) = 60	φ(94) = 46	φ(95) = 72
φ(96) = 32	φ(97) = 96	φ(98) = 42	φ(99) = 60	φ(100) = 40

How to use the Euler's Totient function calculator

The procedure to use the Euler’s Totient function calculator is as follows:

1Enter the positive integer n.
2Click Calculate button to calculate the value of Euler's Totient function n.
3Click the Reset button to start a new calculation.

Solved examples using the Euler's Totient function calculator

Example 1: Find φ(360) value.

Enter 360 into the input box and click Calculate button, as shown in the figure, the value of φ(360) is 96.

φ(360) = 96

the value of φ(360) euler's totient function

Example 2: What is the value of φ(437)?

Enter 437 into the input box and click Calculate button, as shown in the figure, the value of φ(437) is 396.

φ(437) = 396

the value of φ(437) euler's totient function

Euler's Totient Function Calculator