Euler Phi Function/Examples/24

Example of Euler $\phi$ Function of Square-Free Integer

 * $\map \phi {24} = 8$

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:
 * $24 = 2^3 \times 3$

Thus: