Question:
The remainder when \(3^{2022}\) is divided by 5 is :
The remainder when \(3^{2022}\) is divided by 5 is :
Show Hint
Use the cycle of powers of 3 modulo 5, which repeats every 4 steps.
Updated On: Nov 4, 2026
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The Correct Option is D
Solution and Explanation
\(3^1 \equiv 3,\ 3^2 \equiv 4,\ 3^3 \equiv 2,\ 3^4 \equiv 1 \pmod 5\), so the cycle length is 4.
\(2022 = 4 \times 505 + 2\), hence \(3^{2022} \equiv (3^4)^{505}\cdot 3^2 \equiv 1 \cdot 9 \equiv 4 \pmod 5\).
Answer: (4) 4
\(2022 = 4 \times 505 + 2\), hence \(3^{2022} \equiv (3^4)^{505}\cdot 3^2 \equiv 1 \cdot 9 \equiv 4 \pmod 5\).
Answer: (4) 4
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