# C++ program to find factorial of a number

The factorial function is a mathematical formula represented by an exclamation mark "!". In the Factorial formula you must multiply all the integers and positives that exist between the number that appears in the formula and the number 1.

#### Here’s an example:

5! = 1 * 2 * 3 * 4 * 5 = 120
On this formula number 5 will be called 5th factorial and multiplied by all the numbers that appear on the example until number 1.

#### Calculating From the Previous Value (Recursive Program)

We can easily calculate a factorial from the previous factorial value
To work out 5!, multiply 5 by 4! to get 120 here 4! = 1*2*3*4 = 24
To work out 4!, multiply 4 by 3! to get 24 here 3! = 1*2*3 = 6
To work out 3!, multiply 3 by 2! to get 6 here 2! = 1*2 = 2
To work out 2!, multiply 2 by 1! to get 2 here 1! = 1
To work out 1!, multiply 1 by 0! to get 1 here 0! = 1
So the rule is:
n! = n × (n−1)!
Which says
"the factorial of any number is that number times the factorial of (that number minus 1)"
So 7! = 7 × 6!, ... and 123! = 123 × 122!, etc.

### Example: C++ program to find factorial

For loop runs from 1 to n. For each iteration of  the loop, factorial is multiplied with i. Then the final value of factorial is the product of all numbers from 1 to n.

#### Output

Enter a positive integer: 5
Factorial of 5 is 120

### Example: C++ program to find factorial using a function

For loop runs from 1 to n. For each iteration of  the loop, factorial is multiplied with i. Then thefinal value of factorial is the product of all numbers from 1 to n.

#### Output

Enter a positive integer: 5
Factorial of 5 is 120

### Example: C++ program to find factorial using a Recursive Program

If the number is 0 or 1 then factorial() returns 1. If any other number, then factorial() recursively calls itself with the value n-1 i.e factorial(n-1).

#### Output

Enter a positive integer: 5
Factorial of 5 is 120