Question

Find the number of zeros in the product 56⁹⁹ × 125⁸⁹.
1. 267
2. 99
3. 89
4. 297

Answer 1

Correct Answer - Option 1 : 267

Concept Used:

Number of zeros = Number of pairs of 2 × 5

Calculation:

56⁹⁹ × 125⁸⁹ = (2³ × 7)⁹⁹ × (5³)⁸⁹

⇒ 2²⁹⁷ × 7⁹⁹ × 5²⁶⁷

⇒ (2 × 5)²⁶⁷ × 2³⁰ × 7⁹⁹

⇒ 10²⁶⁷ × 2³⁰ × 7⁹⁹

∴ The number of zeros in the given product is 267.

Short Trick:

In the case of only multiplication

No. of Zeros = min {a, b} where a is the maximum power of 2 and b is the maximum power of 5.

No. of Zeros = min {297, 267} = 267