Factorial Program in C

The factorial of a number, denoted as 'n!', is the product of all positive integers up to n. Essential in permutations, combinations, and probability, it simplifies complex calculations, like determining possible seating arrangements

Algorithm of C Program for Factorial

Let us go through the algorithm of C program to find factorial of a number

• Take input the number n from the user whose factorial is to be calculated.
• We start from n, decrease its value to 1, and keep multiplying the value achieved at each stage.
• The final value obtained when n becomes 1 is equal to our factorial.

Factorial Program Using For Loop

Now we shall see how to write a program to find the factorial of a number.

To calculate the factorial of a number n, we have to multiply all the numbers from 1 to n. We can do this with the help of a for loop. We use a variable called fact in which our factorial will be stored. We initialize fact as 1.

We run a for loop from i = 1 to i <= n, and at each step, multiply i with our fact variable. We then print our fact variable to the screen.

Input : 5

Output: Factorial of 5 is: 120

Explanation:

Let us understand the code with the help of the given example. Here the input is 5. We are using a for loop to traverse from i = 1 to i <= 5, and at each step, i is multiplied with our fact variable.

• When, i = 1, fact = 1.
• When i = 2, fact = 1 X 2 = 2.
• When i = 3, fact = 2 X 3 = 6.
• When i = 4, fact = 6 X 4 = 24.
• When i = 5, fact = 24 X 5 = 120.*

In this way, we are calculating our factorial using for loop. If the given number is n, our loop will execute n times. Thus, the time complexity is O(N).

C Program for Factorial Using While Loop

We can also use a while loop instead of a for loop to write a program to find factorial of a number in this we loop through all the numbers from one to n and calculate the factorial. We use a variable called fact in which our factorial will be stored. We initialize fact as 1. We also use another variable i, and initialize i as 1.

We run our while loop while i <= n, and at each step, multiply i with our fact variable. The value of i is incremented by 1 at each step. We come out of the while loop and print our fact variable to the screen.

Input : 5

Output:

Explanation: Let us understand the C program to find factorial of a number with the help of the given example. Here the input is 5. At first, our i is set to 1. We are using a while loop at each step of which i is multiplied by our fact variable and incremented by 1.

*When, i = 1, fact = 1, i becomes 2.

• When i = 2, fact = 1 X 2 = 2, i becomes 3.
• When i = 3, fact = 2 X 3 = 6, i becomes 4.
• When i = 4, fact = 6 X 4 = 24, i becomes 5.
• When i = 5, fact = 24 X 5 = 120, i becomes 6.
• i is no longer less than equal to 5. Thus, we come out of the while loop and print 120 to the screen.

In this way, we are calculating our factorial using a while loop.

If the given number is n, our loop will execute n times. Thus, the time complexity is O(N).

Factorial Program Using Recursion

Now let's see the factorial program in C using recursion. The function will keep on calling itself until a base condition is reached. Let us see how to write a program to find the factorial of a number.

We use a recursive function and pass the number whose factorial is to be calculated, say n. The recursive function will call itself with descending values, n-1, n-2, n-3, and all the way till 1. At each step, it will multiply the values to calculate the factorial.

Input : 4

Output:

Explanation:

Let us understand the above C program to find factorial of a number with the help of the input. If we are to calculate the factorial of 4, this is how the flow of the recursive call will be:

fact(4) = 4 X fact(3) = 4 X 3 X fact(2) = 4 X 3 X 2 X fact(1) = 4 X 3 X 2 X 1 X fact(0) = 4 X 3 X 2 x 1 //since fact(0) will return 1. = 24

In this way, we are using recursion to calculate the factorial of a number in C.

The recursive function will be called n-1 times, and at each time, the value of n is decremented by 1. Thus the time complexity of the above program will be O(N).

C Program for Factorial Using Ternary Operator

The ternary operator is a shorthand way of using if-else. It takes three arguments:

• The comparison argument
• The result value if the comparison is true
• The result value if the comparison is false

Let us see how we can use the ternary operator to write the factorial program in C.

• We shall check if n equals 1 or 0.
• If it is true, we shall return 1.
• If it is false, we shall return n X fact(n-1).

This can be done by the following single line of code: return (n == 1 || n == 0) ? 1 : n factorial(n - 1);

The flow of this program would be similar to the recursive program. Only the if condition of the recursive function is replaced with the ternary operator.

Input : 4

Output:

Explanation:

We have already seen the flow of the recursive function. The flow of the factorial program using c ternary operator is similar. At each step, the function will check if n is equal to 0 or 1. If so, then it will return 1, else it will return n X fact(n-1). Since the function is running N times, the time complexity of the above program will be O(N).