Question

Find the number of zeros in n! where n is a number between 100 and 105.
1. 20
2. 21
3. 23
4. 24

Answer 1

Correct Answer - Option 4 : 24

Given:

number between 100 and 105

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 101, 102, 103, and 104. The number of zeros will be the same for any value because 5 does not occur between 100 and 105.

Let n = 102

102! = 102 × 101 × … × 1

Maximum power of 5 in 102! = 102/5 + 102/5² = 20 + 4 = 24

Here we consider integer values only and ignore the remainder.

∴ The number of zeros is 24.