If 10^68 is divided by 13 , the remainder is
Started 4 hours ago by Admin in
Explanatory Answer
Question:
If 10^68 is divided by 13, what is the remainder?
Solution:
We calculate remainders of powers of 10 modulo 13:
10^1 mod 13 = 10
10^2 mod 13 = 9
10^3 mod 13 = 12
10^4 mod 13 = 3
10^5 mod 13 = 4
10^6 mod 13 = 1
So, after every power of 6, the remainders repeat in a cycle: {10, 9, 12, 3, 4, 1}.
Now, 68 ÷ 6 = 11 remainder 2.
Thus, 10^68 mod 13 corresponds to the 2nd element in the cycle, which is 9.
Answer: 9
-
No one is replied to this question yet. Be first to reply!
Previous year papers
2024
2023
2022
2021
2020
2019
2018