2019 · Q86
If 10ⁿ divides 6²³ × 75⁹ × 105², then what is the largest value of n?
Elementary MathematicsNumber System
- A20
- B22
- C23
- D28
Explanation
Factor: 6²³ × 75⁹ × 105² = (2·3)²³ × (3·5²)⁹ × (3·5·7)² = 2²³·3³⁴·5²⁰·7². Since 10ⁿ = 2ⁿ·5ⁿ, n is limited by the scarcer of 2s and 5s: min(23, 20) = 20. The answer is (A).