Question

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

Answer 1

Answer:

2

Step-by-step explanation:

Find the remainder when 2 power 81 is divided by 17​

2⁸¹

= 2⁸⁰ * 2

= 2⁴ˣ²° * 2

= (2⁴)²⁰ * 2

= (16)²⁰ * 2

2⁸¹/17 Reminder

= (-1)²⁰ * 2

= 1 * 2

= 2

Answer 2

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.