If $\phi (n)$ represents Euler quotient function, then what is the value of $\phi (77)$ ?
Answer & explanation
Correct answer: option 3
The correct answer is option (3) : 60
77 = 7 × 11 (both are prime numbers)
Using Euler’s totient formula:
ϕ(n) = n(1 − 1/p)(1 − 1/q)
ϕ(77) = 77(1 − 1/7)(1 − 1/11)
= 77 × (6/7) × (10/11)
= 66 × (10/11)
= 60