Question

find the remainder when 2^81 is divided by 7 ​

Answer 1

Answer:

(2^3)×26×8/7

1×8/7

remainder 1

Answer 2

Answer:

Remainder is 2.

Step-by-step explanation:

Given:

Dividend = $2^{81}$

Divisor = 17

To find: Remainder

First we simplify the given dividend

$2^{80}\times2$

$=(2^4)^{20}\times2$

$\imples(16)^{20}\times2$

 

Now, Dividing first factor of the above expression.        

where when 16 is divided by 17 it leave -1 as remainder,

$\implies(-1)^{20}\times2$

$\implies1\times2$

⇒ 2

Now, when dividend is smaller than divisor then remainder is equal to dividend.

So, when 2 is divided by 17 it leaves remainder = 2.

Therefore, Remainder is 2.