If $\phi (n)$ represents Euler quotient function, then what is the value of $\phi (2000)$ ?
Answer & explanation
Correct answer: option 1
The correct answer is option (1) : 800
$\phi (2000)= \phi (2^4×5^2)$
$= \phi (2^4) × \phi (5^3)$
$= (2^4-2^3) (5^3-5^2)$
$= (16-8) (125-25)$
$= 8 × 100$
$= 800$