Remainder of 17²⁰⁰ ÷ 18 — Number System Aptitude Question
Remainder of 17²⁰⁰ ÷ 18: What is the remainder when 17²⁰⁰ is divided by 18? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 45 seconds
Question
What is the remainder when 17²⁰⁰ is divided by 18?
Options
- 1
- 8
- 16
- 17
Show the answer and the worked solution
Correct answer: A. 1
Worked solution
- 17 ≡ −1 (mod 18).
- 17²⁰⁰ ≡ (−1)²⁰⁰ = 1 (mod 18) because the exponent is even.
- The remainder is 1.
Answer: 1.
The idea
A base one less than the divisor is −1 in disguise: even powers give 1, odd powers give the divisor minus 1. Spotting this saves the whole cyclicity calculation.
Shortcut. 17² = 289 = 16 × 18 + 1, so 17² leaves 1, and 17²⁰⁰ = (17²)¹⁰⁰ leaves 1 as well.
Common trap. 17 — assuming 17ⁿ always leaves 17; that holds only for odd powers, and 200 is even.