If 3²⁰¹⁹ is divided by 10, then what is the remainder?

Answer: (c) 7

The remainder on division by 10 is simply the last digit. Last digits of powers of 3 repeat as 3, 9, 7, 1, and 2019 leaves remainder 3 on division by 4, so 3²⁰¹⁹ ends in 7.

1. The last digit of 3¹, 3², 3³, 3⁴ is 3, 9, 7, 1, and this cycle of 4 repeats.
2. 2019 = 4 × 504 + 3, so 3²⁰¹⁹ has the same last digit as 3³.
3. 3³ = 27 ends in 7.
4. The remainder on dividing by 10 equals the last digit, so the remainder is 7.
5. Check: 3⁷ = 2187 also ends in 7, and 7 = 4 + 3 — the pattern holds.

Remember · Remainder by 10 = units digit. For powers of 2, 3, 7, 8 the units digit cycles every 4, so use the exponent's remainder by 4.

Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). · Report an error