# 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.