Question

What is the reminder when 10^200 is divided by 8?

Answer 1

Answer:

0

Step-by-step explanation:

10^3 = 1000 = 8 * 125 is a multiple of 8

10^200 = 10^197 * 10^3 and hence is also a multiple of 8. Hence reminder is 0 when dividing it by 8

Answer 2

Given:

A number in the exponential form 10^200.

To Find:

The remainder when the above number is divided by 8.

Solution:

The given number can be solved using the factorization method.

1. The given number is 10^200.

2. The given number can be also written as,

=> 10 x 10 x 10 x 10 x 10^196,

=> 2 x 5 x 2 x 5 x 2 x 5 x 2 x 5 x 10^196,

=> 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5 x 10^196,

=> 8 x 5^4 x 10^196.

3. From the above factorization it is clear that 8 is also a factor of 10^200. Hence, when the dividend is a factor of the divisor the remainder is 0 in all the cases. Hence the remainder, in this case, is 0.

Therefore, the remainder when 10^200 is divided by 8 is 0.