Aptitude Discussion

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

✖ A. |
143 |

✖ B. |
243 |

✔ C. |
343 |

✖ D. |
443 |

**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 $1×343 =\textbf{343}$

**Shreyash Okhade**

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

@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.

how to solve this kind of question