2021 · Q92
What is the remainder when 2¹⁰⁰⁰⁰⁰⁰ is divided by 7?
Elementary MathematicsNumber System
- A1
- B2
- C4
- D6
Explanation
Since 2³ = 8 ≡ 1 (mod 7), 2^1000000 = 2·(2³)^333333 ≡ 2·1 = 2 (mod 7). The remainder is 2. Hence option B.
What is the remainder when 2¹⁰⁰⁰⁰⁰⁰ is divided by 7?
Explanation
Since 2³ = 8 ≡ 1 (mod 7), 2^1000000 = 2·(2³)^333333 ≡ 2·1 = 2 (mod 7). The remainder is 2. Hence option B.