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Quantitative Aptitude

Divisibility Rule for Composite Numbers

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Question

What is remainder when $7^{84}$ is divided by 2402?

A

1

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B

6

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C

2401

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D

None of these

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Solution

The correct option is B 2401
$7^{84}$
$= (7^{4})^{21}$
$= (2401)^{21}$
$= (2402 - 1)^{21}$
$= 2402 K + (- 1)^{21}$
$= 2402 K - 1$
Hence,the remainder when $7^{84}$ is divided by $2402$ is equal to $- 1$ or $2402 - 1$
$= 2401.$

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