2023 · Q2
What is the largest power of 10 that divides the product 29 × 28 × 27 ×...2 × 1?
Elementary MathematicsNumber System
- A4
- B5
- C6
- D7
Explanation
The largest power of 10 dividing 29! equals the exponent of 5 in 29!, since factors of 2 are plentiful. By Legendre's formula this is ⌊29/5⌋ + ⌊29/25⌋ = 5 + 1 = 6. So 10^6 is the largest power of 10 dividing the product (C).