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