Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720.
Recursive Solution:
Factorial can be calculated using following recursive formula.
n! = n * (n-1)! n! = 1 if n = 0 or n = 1
Following is implementation of factorial.
C++
// C++ program to find factorial of given number #include <iostream> using namespace std; // function to find factorial of given number unsigned int factorial(unsigned int n) { if (n == 0) return 1; return n * factorial(n - 1); } // Driver code int main() { int num = 5; cout << "Factorial of " << num << " is " << factorial(num) << endl; return 0; } // This code is contributed by Shivi_Aggarwal |
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C
// C program to find factorial of given number #include <stdio.h> // function to find factorial of given number unsigned int factorial(unsigned int n) { if (n == 0) return 1; return n * factorial(n - 1); } int main() { int num = 5; printf("Factorial of %d is %d", num, factorial(num)); return 0; } |
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Java
// Java program to find factorial of given number class Test { // method to find factorial of given number static int factorial(int n) { if (n == 0) return 1; return n * factorial(n - 1); } // Driver method public static void main(String[] args) { int num = 5; System.out.println( "Factorial of " + num + " is " + factorial(5)); } } |
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Python3
# Python 3 program to find # factorial of given number # Function to find factorial of given number def factorial(n): if n == 0: return 1 return n * factorial(n-1) # Driver Code num = 5; print("Factorial of", num, "is", factorial(num)) # This code is contributed by Smitha Dinesh Semwal |
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C#
// C# program to find factorial // of given number using System; class Test { // method to find factorial // of given number static int factorial(int n) { if (n == 0) return 1; return n * factorial(n - 1); } // Driver method public static void Main() { int num = 5; Console.WriteLine("Factorial of " + num + " is " + factorial(5)); } } // This code is contributed by vt_m |
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PHP
<?php // PHP program to find factorial // of given number // function to find factorial // of given number function factorial($n) { if ($n == 0) return 1; return $n * factorial($n - 1); } // Driver Code $num = 5; echo "Factorial of ", $num, " is ", factorial($num); // This code is contributed by m_kit ?> |
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Output:
Factorial of 5 is 120
Iterative Solution:
Factorial can also be calculated iteratively as recursion can be costly for large numbers. Here we have shown the iterative approach using both for and while loop.
Using For loop
C++
// C++ program for factorial of a number #include <iostream> using namespace std; // function to find factorial of given number unsigned int factorial(unsigned int n) { int res = 1, i; for (i = 2; i <= n; i++) res *= i; return res; } // Driver code int main() { int num = 5; cout << "Factorial of " << num << " is " << factorial(num) << endl; return 0; } // This code is contributed by Shivi_Aggarwal |
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C
#include <stdio.h> // function to find factorial of given number unsigned int factorial(unsigned int n) { int res = 1, i; for (i = 2; i <= n; i++) res *= i; return res; } int main() { int num = 5; printf( "Factorial of %d is %d", num, factorial(num)); return 0; } |
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Java
// Java program to find factorial of given number class Test { // Method to find factorial of the given number static int factorial(int n) { int res = 1, i; for (i = 2; i <= n; i++) res *= i; return res; } // Driver method public static void main(String[] args) { int num = 5; System.out.println( "Factorial of " + num + " is " + factorial(5)); } } |
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Python3
# Python 3 program to find # factorial of given number # Function to find factorial of given number def factorial(n): res = 1 for i in range(2, n+1): res *= i return res # Driver Code num = 5; print("Factorial of", num, "is", factorial(num)) # This code is contributed by Smitha Dinesh Semwal |
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C#
// C# program to find // factorial of given number using System; class Test { // Method to find factorial // of given number static int factorial(int n) { int res = 1, i; for (i = 2; i <= n; i++) res *= i; return res; } // Driver method public static void Main() { int num = 5; Console.WriteLine( "Factorial of " + num + " is " + factorial(5)); } } // This code is contributed by vt_m |
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PHP
<?php // function to find factorial // of given number function factorial( $n) { $res = 1; $i; for ($i = 2; $i <= $n; $i++) $res *= $i; return $res; } // Driver Code $num = 5; echo "Factorial of ", $num, " is ", factorial($num); // This code is contributed // by anuj_67. ?> |
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Output :
Factorial of 5 is 120
Using While loop
C
// C program for factorial of a number #include <stdio.h> // function to find factorial of given number unsigned int factorial(unsigned int n) { if(n == 0) return 1; int i = n, fact = 1; while (n / i != n) { fact = fact * i; i--; } return fact; } int main() { int num = 5; printf("Factorial of %d is %d", num, factorial(num)); return 0; } |
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C++
// C++ program for factorial of a number #include <iostream> using namespace std; // function to find factorial of given // number using while loop unsigned int factorial(unsigned int n) { if(n == 0) return 1; int i = n, fact = 1; while (n / i != n) { fact = fact * i; i--; } return fact; } // Driver code int main() { int num = 5; cout << "Factorial of " << num << " is " << factorial(num) << endl; return 0; } // This code is contributed by Shivi_Aggarwal |
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Java
// Java program to find factorial of given number class Test { // Method to find factorial of the given number static int factorial(int n) { if(n == 0) return 1; int i = n, fact = 1; while (n / i != n) { fact = fact * i; i--; } return fact; } // Driver method public static void main(String[] args) { int num = 5; System.out.println( "Factorial of " + num + " is " + factorial(5)); } } |
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Python3
# Python 3 program to find # factorial of given number # Function to find factorial of given number def factorial(n): if(n == 0): return 1 i = n fact = 1 while(n / i != n): fact = fact * i i -= 1 return fact # Driver Code num = 5; print("Factorial of", num, "is", factorial(num)) # This code is contributed by Smitha Dinesh Semwal |
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C#
// C# program to find // factorial of given number using System; class Test { // Method to find factorial // of given number static int factorial(int n) { if(n == 0) return 1; int i = n, fact = 1; while (n / i != n) { fact = fact * i; i--; } return fact; } // Driver method public static void Main() { int num = 5; Console.WriteLine( "Factorial of " + num + " is " + factorial(5)); } } |
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Output :
Factorial of 5 is 120
Time complexity of the above iterative solutions is O(n).
One line Solution (Using Ternary operator):
C++
// C++ program to find factorial of given number #include <iostream> int factorial(int n) { // single line to find factorial return (n == 1 || n == 0) ? 1 : n * factorial(n - 1); } // Driver Code int main() { int num = 5; printf("Factorial of %d is %d", num, factorial(num)); return 0; } // This code is contributed by Rithika palaniswamy. |
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Java
// Java program to find factorial // of given number class Factorial { int factorial(int n) { // single line to find factorial return (n == 1 || n == 0) ? 1 : n * factorial(n - 1); } // Driver Code public static void main(String args[]) { Factorial obj = new Factorial(); int num = 5; System.out.println( "Factorial of " + num + " is " + obj.factorial(num)); } } // This code is contributed by Anshika Goyal. |
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Python3
# Python 3 program to find # factorial of given number def factorial(n): # single line to find factorial return 1 if (n == 1 or n == 0) else n * factorial(n - 1) # Driver Code num = 5print ("Factorial of", num, "is", factorial(num)) # This code is contributed # by Smitha Dinesh Semwal. |
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C#
// C# program to find factorial // of the given number using System; class Factorial { int factorial(int n) { // single line to find factorial return (n == 1 || n == 0) ? 1 : n * factorial(n - 1); } // Driver Code public static void Main() { Factorial obj = new Factorial(); int num = 5; Console.WriteLine( "Factorial of " + num + " is " + obj.factorial(num)); } } // This code is contributed by vt_m. |
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PHP
<?php // PHP program to find factorial // of given number function factorial( $n) { // single line to find factorial return ($n == 1 || $n == 0) ? 1: $n * factorial($n - 1); } // Driver Code $num = 5; echo "Factorial of ", $num, " is ", factorial($num); // This code is contributed by anuj_67. ?> |
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Output:
Factorial of 5 is 120
The above solutions cause overflow for small numbers. Please refer factorial of large number for a solution that works for large numbers.
Please write comments if you find any bug in the above code/algorithm, or find other ways to solve the same problem.
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