Question

Find the number of trailing zeros in n! where n lies between 355 and 360.
1. 71
2. 87
3. 90
4. 356

Answer 1

Correct Answer - Option 2 : 87

Given:

n lies between 355 and 360

Concept Used:

n! = n(n – 1)(n – 2)…1

Number of zeros = Power of 5

In the case of factorial, the power of 5 is the limiting factor because 5 is less likely to occur than 2.

Maximum power of 5 in n! = n/5 + n/5² + n/5³ +... (Consider integer values only)
Calculation:

We can pick any value from 356, 357, 358, and 359. The number of zeros will be the same for any value because 5 does not occur from 356 to 359.

Let n = 359

359! = 359 × 358 × … × 1

Maximum power of 5 in 359! = 359/5 + 359/5² + 359/5³ = 71 + 14 + 2 = 87

Here we consider integer values only and ignore the remainder.

∴ The number of zeros is 87.