If $\phi (n)$ represents Euler quotient

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

If $\phi (n)$ represents Euler quotient function, then what is the value of $\phi (80850)$ ?

Options:

16850

16750

16700

16800

Correct Answer:

16800

Explanation:

The correct answer is option (4) : 16800

$\phi (80850) = \phi (2×3×5^2×7^2×11)$

$=\phi (2) .\phi (3).\phi(5^2).\phi(7^2),\phi(11)$

$=(2-1)(3-1)(5^2-5^1).(7^2-7^1)(11-1)$

$=1×2×20×42×10$

$=16800$