If $\phi(n)$ represents Euler's totient function then $\phi(432)$ is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 144
$432 = 2^4 \cdot 3^3$
$\phi(n) = n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)$
$\phi(432) = 432\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)$
$= 432 \cdot \frac{1}{2} \cdot \frac{2}{3}$
$= 432 \cdot \frac{1}{3} = 144$
$\phi(432) = 144$