Euler Phi Function of 30

Example of Use of Euler $\phi$ Function
The value of the Euler $\phi$ function for the integer $30$ is $8$.

Proof
From Euler Phi Function of Integer:
 * $\displaystyle \phi \left({n}\right) = n \prod_{p \mathop \backslash n} \left({1 - \frac 1 p}\right)$

where $p \mathop \backslash n$ denotes the primes which divide $30$.

We have that:
 * $30 = 2 \times 3 \times 5$

Thus: