Question

How to find the remainder when 48 power 565 divided by 7?

Answer 1

remainder will be 6...

Answer 2

Answer:

The remainder when $48^{565}$ is divided by 7 is 6.

Step-by-step explanation:

To find : The remainder when 48 power 565 divided by 7?

Solution :  

The remainder when $48^{565}$ is divided by 7.

Split the term,

$\frac{48^{565}}{7}=\frac{(49-1)^{565}}{7}$

$\frac{48^{565}}{7}=\frac{(7\times 7-1)^{565}}{7}$

As 49 is completely divide by 7 and gave remainder 0 by quotient 7.

We know, $\frac{(ax-1)^n}{a}$ gives remainder -1.

Applying in the form,

$\frac{(-1)^{565}}{7}\rightarrow \frac{-1}{7}$

The required remainder is 7-1=6.

Therefore, The remainder when $48^{565}$ is divided by 7 is 6.