2024 · Q45
What is the remainder when 70 × 71 × 72 × 73 × 74 × 75 × 76 × 77 × 78 × 79 is divided by 1000?
Elementary MathematicsNumber System
- A3
- B2
- C1
- D0
Explanation
Look for factors making the product a multiple of 1000: 70 × 75 = 5250 = 21 × 250. Multiplying further by the even factor 76 gives 5250 × 76 = 399000, which ends in three zeros. Since the full product 70×71×…×79 contains these factors, it is divisible by 1000. The remainder is therefore 0 — option D.