# Easy Number System Solved QuestionAptitude Discussion

 Q. The remainder when $7^84$ is divided by 342 is
 ✖ A. 0 ✔ B. 1 ✖ C. 49 ✖ D. 241

Solution:
Option(B) is correct

Solution:

$\dfrac{7^{84}}{342} = \dfrac{(7^3)^{28}}{342}$

$= \dfrac{(343+1)^{28}}{342}$

According to the remainder theorem it will have the remainder = 1.

Edit: For an alternative solution using 'modulus' method, check comment by Sravan Reddy.

## (2) Comment(s)

Sravan Reddy
()

Using 'modulus' method

7^3 = 343mod342 = (-1)mod342

raising each sides by power 28

(7^3)^28=(-1)^28mod 342

7^84 = 1mod342

reminder = 1

Sravan Reddy
()

Sorry, it's not (-1), it should be +1