Here is a C++ program to find factorial of a number using recursion. In this C++ program, we will find factorial of a number using recursion.
N! = 1 x 2 x 3 x 4....x (N-2) x (N-1) x N
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720. 0! = 1 1! = 1
NOTE : Factorial does not exist for negative numbers and factorial of 0 is 1.
The expression to calculate factorial obeys recursive sub-structure property, hence we can use use recursion to calculate factorial.
Let factorial(N) is a function to calculate the value of N!. To find factorial(N) we can first calculate factorial(N-1) then multiply it with N.
N! = 1 x 2 x 3 x 4....x (N-2) x (N-1) x N N! = (N-1)! x N factorial(N) = factorial(N-1) x N
Function factorial(N) reduces the problem of finding N! into sub-problem of finding (N-1)! first and then multiplying it with N to get N!. It keeps on reducing the domain of the problem until N becomes zero.
C++ program to Calculate Factorial of a Number Using Recursion
#include <iostream>
using namespace std;
int getFactorial(int N);
int main(){
int N;
cout << "Enter a Number\n";
cin >> N;
cout << "Factorial of " << N << " = " <<
getFactorial(N);
return 0;
}
int getFactorial(int N){
// Recursion Termination condition
if(N <= 1){
return 1;
}
return N * getFactorial(N - 1);
}
Output
Enter a Number 5 Factorial of 5 = 120
In above program, we are using a recursive function getFactorial(N) to calculate the factorial of N. If N <= 1, then getFactorial function returns 1, (this is the recursion
termination condition) otherwise, it recursively calls itself to calculate factorial of N-1 and multiply it with N to get N!.
Inside main function, we first take a number as input from user using cin ans store it in a variable N. Then we call getFactorial function by passing N as parameter to calculate N!. Above c++ program cannot be used to calculate factorial of large numbers because factorial of such numbers exceeds the range of int data type.
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