# Euler Phi Function/Examples/Phi is 6

## Example of Use of Euler $\phi$ Function

There are $4$ numbers for which the value of the Euler $\phi$ function is $6$:

$7, 9, 14, 18$

## Proof

From Euler Phi Function of $9$, we already have that $\map \phi 9 = 6$.

### $7$

$\map \phi 7 = 7 - 1 = 6$

### $14$

 $\ds \map \phi {14}$ $=$ $\ds 14 \paren {1 - \dfrac 1 7} \paren {1 - \dfrac 1 2}$ $\ds$ $=$ $\ds 14 \times \dfrac 6 7 \times \dfrac 1 2$ $\ds$ $=$ $\ds 6$

### $18$

 $\ds \map \phi {18}$ $=$ $\ds 18 \paren {1 - \dfrac 1 2} \paren {1 - \dfrac 1 3}$ $\ds$ $=$ $\ds 18 \times \dfrac 1 2 \times \dfrac 2 3$ $\ds$ $=$ $\ds 6$

Hence the result.

$\blacksquare$