Question

Find the remainder when 2^81 is divided by 17

Answer 1

Answer:

Remainder when $2^{81}$ divided by 17 is 2.

Step-by-step explanation:

Given:

Dividend = $2^{81}$

Divisor = 17

To find: Remainder

So, we can write given number as,

$2^{80}\times2$

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

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

         

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.

here, dividend = 2 and divisor = 17

2 < 17 ⇒ Remainder = 2

Therefore, Remainder when $2^{81}$ divided by 17 is 2.