Question

find the remainder when 2 ^81 is divided by 17​

Answer 1

Answer:

Remainder is 2.

Step-by-step explanation:

Given numbers are $2^{81}$ and 17.

To find: Remainder when $2^{81}$ divisible by 17.

We know that 2 has cyclicity of 4.

So, we can write given number as,

$2^{80}\times2$

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

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

         

We also know that

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

So,

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

$\implies1\times2$

⇒ 2

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

Therefore, Remainder is 2.