What is the remainder if  2^192  is divided by 6 ? 

(UPSC CSAT – 2023)

1. 0
2. 1
3. 2
4. 4

Solution: Ans.(4)

2¹⁹² / 6 = (2×2¹⁹¹) / 6 = (2¹⁹¹) / 3

⇒ Rem. (-1)¹⁹¹ ⇒ Rem. (- 1) ⇒ Rem. = 3 – 2 = 2

Final Rem. (2×2) = 4

(Because 2 was the common factor of Dividend and Divisor )

Hence, the correct answer is 4.