Euler Phi Function of 944

Example of Use of Euler $\phi$ Function

$\map \phi {944} = 464$

where $\phi$ denotes the Euler $\phi$ Function.

Proof

From Euler Phi Function of Integer:

$\ds \map \phi n = n \prod_{p \mathop \divides n} \paren {1 - \frac 1 p}$

where $p \divides n$ denotes the primes which divide $n$.

We have that:

$944 = 2^4 \times 59$

Thus:

\(\ds \map \phi {944}\)

\(=\)

\(\ds 944 \paren {1 - \dfrac 1 2} \paren {1 - \dfrac 1 {59} }\)

\(\ds \)

\(=\)

\(\ds 944 \times \frac 1 2 \times \frac {58} {59}\)

\(\ds \)

\(=\)

\(\ds 8 \times 58\)

\(\ds \)

\(=\)

\(\ds 464\)

$\blacksquare$