The value of the Euler Totient function φ (n) at 400 is :

The correct answer is Option (4) → 160

$400=2^4×5^2$

$\phi(n)=n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)....\left(1-\frac{1}{p_n}\right)$

$\phi(400)=400×\left(1-\frac{1}{2}\right)\left(1-\frac{1}{5}\right)$

$=400×\frac{1}{2}×\frac{4}{5}=160$