Q. What is the remainder if 2^192 is divided by 6?
(a) 0
(b) 1
(c) 2
(d) 4
Correct Answer: (d) 4
Question from UPSC Prelims 2023 CSAT
Explanation :
The powers of 2 cycle in a pattern of 4 when divided by 6.
Specifically, the remainders are 2, 4, 2, 0, 2, 4, 2, 0, and so on. This pattern repeats every 4 powers.
Since 192 is a multiple of 4, the remainder when 2^192 is divided by 6 is the same as the remainder when 2^4 is divided by 6, which is 4.
So, the answer is (d) 4.
