**Factorial program in c++ **is a simple program which is cpp program to find factorial of number in C++.

In this tutorial** we will see program to find factorial in cpp,Factorial of given number** is the mathematical problem.

**Factorial of a number **

Factorial of a number N is calculated as N!.

**Syntax to find factorial of a number**

factorial

**N!** => N*(N-1)*(N-2)….

**Example: **

Find factorial

**calculate 6 factorial**

**6! =6*5*4*3*2*1 =720**

factorial of a number 6 is 720.

Using this technique we implement the **factorial in cpp**.

We implement **factorial program in cpp** in three ways as :

**Factorial using for loop****Factorial using recursion****Factorial using function.**

**Lets see Factorial in cpp**

**Factorial using for loop**

This is first method using which we implement the factorial.

In this technique, we use the iterative loop as **for loop** to iterate and multiply the number up to N-1.

**Write a program to find factorial of a number**

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#include <iostream> using namespace std; int main() { int c, n, fact = 1; cout<<"Enter a number to calculate its factorial\n"; cin>>n; for (c=1;c<=n;c++) fact=fact*c; cout<<"Factorial of "<<n<<"= "<<fact; return 0; } |

**Output :**

**Explanation :**

**Factorial using for loop**

**1. Execution starts with the main method.**

**2. Declare variables**

c,fact = > temporary variables

n => to store number

**3. First we take input number which user want to find factorial**

cin>>n; => n=3

**4. Next we calculate the factorial using for loop**

for (c=1;c<=n;c++)

**At Iteration 1 :**

c=1, 1<=3 condition true loop executed

fact=fact*c; => fact= 1

**At Iteration 2 :**

c=2, 2<=3 condition true loop executed

fact=fact*c; => fact= 2

**At Iteration 3 :**

c=3, 3<=3 condition true loop executed

fact=fact*c; => fact= 6

**At Iteration 4 :**

c=4, 4<=3 condition false

**5. Print the factorial of number.**

=> cout<<“Factorial of “<<n<<“= “<<fact;

**Factorial using recursion**

**Recursion **: This is second method using which we implement program to find factorial.

In this technique, we recursively call the same function to find factorial.

**What is Recursion** : **Function calling itself is referred as recursion**.

**Factorial program in c++ using recursion **

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#include <iostream> using namespace std; long factorial(int); int main() { int n; long f; cout<<"Enter an integer to find its factorial\n"; cin>>n; if (n < 0) cout<<"Factorial of negative integers isn't defined.\n"; else { f = factorial(n); cout<<n<<"! = "<<f; } return 0; } long factorial(int n) { if (n == 0) return 1; else return(n * factorial(n-1)); } |

**Output :**

**Explanation :**

**Factorial using recursion**

**1. Execution starts with the main method.**

**2. Declare variables**

n => to store number

f => to store factorial

**3. First we take input number which user want to find factorial**

cin>>n; => n=3

**4. Next we check number is valid **

if (n < 0) condition false

else executed

**5. We call recursive function **

f = factorial(n) => factorial(3)

**6 . Control transferred to function **

long factorial(int n) {

if (n == 0) condition false

else

return(n * factorial(n-1));

=> 3*factorial(2); => function get call itself with n=2

we get value 6 => 3*factorial(2); => function get call itself with n=1

we get value 6 => 3*factorial(1); => function get call itself with n=0

if (n == 0) condition true retur 1;

=> 1*2*3 each function call returns multiplication to main

} => returns 6 to main

**7. Print factorial of number returned by function**

=> cout<<n<<“! = “<<f;

**Factorial using function **

This is third method using which we implement the factorial.

__Function __ : Function is a block of statement.

**Factorial program in c++ using function**

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#include <iostream> using namespace std; long factorial(int); int main() { int number; long fact = 1; cout<<"Enter a number to calculate its factorial\n"; cin>>number; cout<<number<<"! = "<<factorial(number); return 0; } long factorial(int n) { int c; long result = 1; for (c = 1; c <= n; c++) result = result * c; return result; } |

**Output :**

**Explanation :**

**Factorial using function**

**1. Execution starts with the main method.**

**2. Declare variables**

number => to store number

fact => to store factorial

**3. First we take input number which user want to find factorial**

cin>>number; => number=3

4. Next call the user defined function factorial(number)

long factorial(int n) => factorial(int 3)

c => teary local variable

result = 1 => store result local variable

for (c = 1; c <= n; c++)

**At Iteration 1 :**

c=1, 1<=3 condition true loop executed

result = result * c; => result =1

**At Iteration 2 :**

c=2, 2<=3 condition true loop executed

result = result * c; => result =2

**At Iteration 3 :**

c=3, 3<=3 condition true loop executed

result = result * c; => result =6

**At Iteration 4 :**

c=4, 4<=3 condition false

return result; => returns 6 to main function

**7. Print factorial of number returned by function**

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