# number of trailing zeros in a factorial of a number.

To find the number of trailing zeros in the factorial of a number, we need to count the number of times the factorial is divisible by 10. This is because each trailing zero represents a factor of 10 in the factorial.

Here is a step-by-step explanation of how to find the number of trailing zeros in the factorial of a number in Ruby:

- Initialize a variable
`count`

to 0. This variable will keep track of the number of trailing zeros. - Start a loop to calculate the factorial of the given number.
- Within the loop, multiply the current value of the factorial by the loop counter variable.
- Check if the current value of the factorial is divisible by 10.
- If it is divisible by 10, increment the
`count`

variable by 1 and divide the factorial by 10. - Repeat steps 4 and 5 until the factorial is no longer divisible by 10.
- Finally, return the value of the
`count`

variable, which represents the number of trailing zeros in the factorial of the given number.

Here is an example code snippet in Ruby that implements the above steps:

```
def count_trailing_zeros(n)
count = 0
factorial = 1
for i in 1..n
factorial *= i
end
while factorial % 10 == 0
count += 1
factorial /= 10
end
return count
end
# Example usage:
n = 10
trailing_zeros = count_trailing_zeros(n)
puts "Number of trailing zeros in the factorial of #{n} is: #{trailing_zeros}"
```

In this example, we define a method `count_trailing_zeros`

that takes an input `n`

representing the number for which we want to find the factorial. We initialize the `count`

variable to 0 and the `factorial`

variable to 1. We then use a loop to calculate the factorial of `n`

by multiplying the current value of the factorial by the loop counter variable. After calculating the factorial, we use a while loop to check if the factorial is divisible by 10. If it is, we increment the `count`

variable by 1 and divide the factorial by 10. This process continues until the factorial is no longer divisible by 10. Finally, we return the value of the `count`

variable, which represents the number of trailing zeros in the factorial of the given number.

Note: The example code assumes that the input number `n`

is a non-negative integer.