How to Find the Factorial of a Number

In mathematics, we often encounter the concept of factorial denoted as n! which represents the product of all integers less, than, or equal to a given non-negative integer n. Factorials find applications in combinatorics, probability, and other mathematical fields. In the R programming language, you have options to calculate factorials using either built-in functions or your own custom code.

Here are some key concepts related to factorials

1. Factorial refers to the product of all integers from 1 up to a number.

2. Recursive Approach: This involves solving problems by breaking them into subproblems that follow a similar pattern.

3. Iterative Approach: Alternatively we can compute factorials using loops and repetitive structures.

To calculate the factorial of a number, in R you can follow these steps:

a) Utilizing the built-in function ():

1. Choose the number for which you wish to find its value.

2. Apply the factorial() function to compute the desired result.

3. Print out the obtained value.

R

#Using factorial function
#Using factorial function
num <- 5
factorial_result <- factorial(num)
print(paste("Factorial of", num, "is", factorial_result))

Output:

Factorial of 5 is 120

b) Creating a custom function ( iterative):

1. Define your function that accepts an input number as an argument.

2. Check if the input is either 0 or 1; if so return 1 (base case).If the number provided is, than 1 you can. Use iteration to calculate the factorial. Once you have computed the value make sure to return it.

R

#Iterative factorial function
iterative_factorial <- function(n) {
  result <- 1
  for (i in 1:n) {
    result <- result * i
  }
  return(result)
}

num <- 7
factorial_result_iterative <- iterative_factorial(num)
print(paste("Factorial of", num, "using iterative approach is",
            factorial_result_iterative))

Output:

Factorial of 7 using iterative approach is 5040

• We assigns the value 7 to the variable num.
• factorial_result_iterative <- iterative_factorial(num):
• This calculates the factorial of the number stored in num using the iterative_factorial function.
• The result is stored in the variable factorial_result_iterative.
• print(paste("Factorial of", num, "using iterative approach is", factorial_result_iterative)):
• This line constructs a message that includes the original number, the fact that the calculation is done using the iterative approach, and the calculated factorial value.
• The paste() function combines these components into a single message.

c)Creating a custom function ( Recursive):

1. Define your function that accepts an input number as an argument.

2. Check if the input is either 0 or 1; if so return 1 (base case).If the number provided is, than 1 you can. Use recursion to calculate the factorial. Once you have computed the value make sure to return it.

R

# Recursive factorial function
recursive_factorial <- function(n) {
if (n == 0 || n == 1) {
    return(1)
} else {
    return(n * recursive_factorial(n - 1))
}
}

num <- 6
factorial_result_recursive <- recursive_factorial(num)
print(paste("Factorial of", num, "using recursive approach is",
            factorial_result_recursive))

Output:

Factorial of 6 using recursive approach is 720

• First assigns the value 6 to the variable num.
• factorial_result_recursive <- recursive_factorial(num):
• This calculates the factorial of the number stored in num using the recursive_factorial function.
• The result is stored in the variable factorial_result_recursive.
• print(paste("Factorial of", num, "using recursive approach is", factorial_result_recursive)):
• This line constructs a message that includes the original number, the fact that the calculation is done using the recursive approach, and the calculated factorial value.
• The paste() function combines these components into a single message.
• The print() function then outputs the message to the console.