Unit digit of a product of powers — Aptitude Question
Unit digit of a product of powers: What is the unit digit of 3⁴⁷ × 7²³? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the unit digit of 3⁴⁷ × 7²³?
Options
- 1
- 3
- 7
- 9
Show the answer and the worked solution
Correct answer: A. 1
Worked solution
- Unit digits of 3ⁿ cycle as 3, 9, 7, 1. 47 mod 4 = 3, so 3⁴⁷ ends in 7.
- Unit digits of 7ⁿ cycle as 7, 9, 3, 1. 23 mod 4 = 3, so 7²³ ends in 3.
- 7 × 3 = 21, whose unit digit is 1.
Answer: 1.
The idea
Unit digits of powers cycle with period 4 (or shorter). Take the exponent mod 4 — treating a remainder of 0 as the 4th position — for each factor, then multiply just the unit digits.
Shortcut. Pair them: 3²³ × 7²³ = 21²³ ends in 1, leaving 3²⁴ = 81⁶, which also ends in 1.
Common trap. 9 — reading 3⁴⁷ as ending in 3 (as if 47 left 1 on division by 4) and multiplying by the 3 from 7²³.