Euler Phi Function of 420

Example of Use of Euler $\phi$ Function

 * $\phi \left({420}\right) = 96$

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

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 $n$.

We have that:
 * $420 = 2^2 \times 3 \times 5 \times 7$

Thus: