Question

Remainder 3^703 is divided by 80 is _______

Answer 1

Answer:

27

Step-by-step explanation:

It's said that 3^703 is divided by 80.

To find the remainder.

We need to first divide 703 by 80 and find the remainder.

=> 703 = 80 × 8 + 63

Clearly, 63 is remainder when 703 is divided by 80.

Now, divide 63 by 4 because powers of 3 give same last digits after power 4.

For example,

• 3 , 9, 27, 81, 243

In 243 , last term is 3 which is repeated after 4 powers.

Dividing 63 by 4 , we get,

=> 63 = 4 × 15 + 3

Here, remainder is 3.

So, the required remainder will be 3^3, i.e, 27.

Hence, the required value is 27.

Answer 2

Answer:

703 = 80 × 8 + 63

Clearly, 63 is remainder when 703 is divided by 80.

Now, divide 63 by 4 because powers of 3 give same last digits after power 4.

For example,

3 , 9, 27, 81, 243

In 243 , last term is 3 which is repeated after 4 powers.

Dividing 63 by 4 , we get,

=> 63 = 4 × 15 + 3

Here, remainder is 3.

So, the required remainder will be 3^3, i.e, 27.

Hence, the required value is 27.

Step-by-step explanation: