2025 · Q37
Given that (100× 99× 98× …× 3× 2× 1)/(100ⁿ) is an integer. What is the largest value of n for which this is true?
Elementary MathematicsNumber System
- A20
- B21
- C24
- DNone of these
Explanation
100! contains 100ⁿ = 2²ⁿ·5²ⁿ. The exponent of 5 in 100! is ⌊100/5⌋ + ⌊100/25⌋ = 20 + 4 = 24, so we need 2n ≤ 24, i.e. n ≤ 12. None of the listed values 20, 21, 24 satisfies this, so the answer is 'None of these', option (d).