Remainder of 3²¹ ÷ 5 — Number System Aptitude Question
Remainder of 3²¹ ÷ 5: What is the remainder when 3²¹ is divided by 5? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
What is the remainder when 3²¹ is divided by 5?
Options
- 1
- 2
- 3
- 4
Show the answer and the worked solution
Correct answer: C. 3
Worked solution
- Remainders of 3ⁿ mod 5 cycle: 3, 4, 2, 1.
- 21 mod 4 = 1, so 3²¹ sits at the first position of the cycle.
- The remainder is 3.
Answer: 3.
The idea
Find the cycle by computing the first few powers, then use the exponent modulo the cycle length — remembering that a remainder of 0 means the last position, not the first.
Shortcut. A remainder on division by 5 follows from the unit digit. 3²¹ ends in 3 (21 leaves 1 on division by 4), and a number ending in 3 leaves 3.
Common trap. 1 — stopping at 3²⁰ = (3⁴)⁵, which leaves 1, and forgetting the one extra factor of 3.