What is the remainder when $7^{7} + 7^{77} + 7^{777} + 7^{7777} . . . . . . . . . + 7^{77777777}$ is divided by 8?

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
0

$\frac{7}{8}$ remainder = -1

Thus, any odd power of 7, when divided by 8, will give a remainder of -1 itself.

$\frac{(- 1)^{7} + (- 1)^{77} + (- 1)^{777} . . . . . .}{8}$

= -1-1-1-...8 times = - 8

The remainder when -8 is divided by 8, is 0.

Suggest Corrections

Similar questions

(1)^{7} + (71)^{77} + (771)^{777} + (7771)^{7777} + (77771)^{77777} + (777771)^{777777}

7 + 77 + 777 + 7777 + \dots

Join BYJU'S Learning Program