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:

  1. Initialize a variable count to 0. This variable will keep track of the number of trailing zeros.
  2. Start a loop to calculate the factorial of the given number.
  3. Within the loop, multiply the current value of the factorial by the loop counter variable.
  4. Check if the current value of the factorial is divisible by 10.
  5. If it is divisible by 10, increment the count variable by 1 and divide the factorial by 10.
  6. Repeat steps 4 and 5 until the factorial is no longer divisible by 10.
  7. 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.