2024 · Q25
What is the smallest natural number n such that (n + 1) × n × (n - 1) × (n - 2) × ... 3 × 2 × 1 is divisible by 910?
Elementary MathematicsNumber System
- A91
- B90
- C13
- D12
Explanation
910 = 2 × 5 × 7 × 13, so (n+1)! must contain the prime 13. That needs n + 1 ≥ 13, so the smallest such n is 12, option (d).