Multiple choice general knowledge math & puzzles

What is the remainder when 7^2001 is divided by 14??

  1. 1

  2. 0

  3. 13

  4. 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need 7^2001 mod 14. Note that 7 mod 14 = 7, and 7² = 49, which gives 49 mod 14 = 7 (since 49 = 3×14 + 7). Similarly, 7³ mod 14 = 7² × 7 mod 14 = 7 × 7 mod 14 = 7. By induction, all positive powers of 7 give remainder 7 when divided by 14. Therefore, 7^2001 mod 14 = 7. Option D is correct. Option A would be true if dividing by 6, and Option B incorrectly assumes divisibility.

Keep practicing — related questions