Q. If 3^2019 is divided by 10, then what is the remainder?
(a) 1
(b) 3
(c) 7
(d) 9
Correct Answer: (c) 7
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
Remainder Calculation for 3^2019
When you divide any power of 3 that is a multiple of 4 by 10, the remainder is always 1.
Since 2016 is a multiple of 4 and the closest multiple of 4 to 2019, we can write 3^2019 as (3^2016)*(3^3).
The remainder when 3^2016 is divided by 10 is 1, and the remainder when 27 (3^3) is divided by 10 is also 7.
Therefore, when you multiply these two remainders together (1*7=7) and divide the result (7) by 10, you get a final remainder of 7.
