Find the number of trailing zeros in 76!

Given:

Find the number of trailing zeros in 76!

Concept:

The number of trailing zeros in a factorial is determined by the number of times 10 is a factor in the number. Since 10 = 2 × 5, and there are always more factors of 2 than 5 in a factorial, we only need to count the number of times 5 is a factor.

Formula Used:

To find the number of trailing zeros in n!, we use the formula:

Number of trailing zeros = ⌊n/5⌋ + ⌊n/5²⌋ + ⌊n/5³⌋ + ...

Calculation:

We have,

⇒ n = 76

⇒ Number of trailing zeros = ⌊76/5⌋ + ⌊76/5²⌋ + ⌊76/5³⌋

⇒ Number of trailing zeros = ⌊76/5⌋ + ⌊76/25⌋ + ⌊76/125⌋

⇒ Number of trailing zeros = 15 + 3 + 0

⇒ Number of trailing zeros = 18

∴ The correct answer is option 1.