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.