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Q.

What is the remainder when $7^{187}$ is divided by $800$?

 A.

143

 B.

243

 C.

343

 D.

443

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Solution:
Option(C) is correct

$7^{187} = (7^4)^{46} × 7^3 = (2401)^{46}×343$

Now $2401 = 2400+1$, where $2400$ is perfectly divisible by $800$

$\Rightarrow (2401)^{46}$ is divided by $800$, the remainder must be $1$

So, the remainder when $7^{187}$ is divided by $800$ is $1×343 =\textbf{343}$


(3) Comment(s)


Shreyash Okhade
 ()

how to solve this kind of question


Kavya
 ()

what about 343? don't we need it to be divided? Please explain an another way of solving this, thank you.

Rithik
 ()

@Kavya: It needs to be divided and that is how the answer is obtained.

If we divide, 343 by 800, we get 343 as the remainder. Which when multiplied by 1 remains 343 only, which is the final answer.

Instead of looking for shortcut method if you learn the concept of CYCLICITY, solving such questions will be a matter of child's play for you.