If $\phi (n)$ represents Euler quotient

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Target Exam

CUET

Subject

Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

If $\phi (n)$ represents Euler quotient function, then what is the value of $\phi (77)$ ?

Options:

100

Correct Answer:

Explanation:

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