#### Here’s an example:

5! = 1 * 2 * 3 * 4 * 5 = 120On 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 valueTo work outSo the rule is:5!, multiply5by4!to get120here4! = 1*2*3*4 = 24

To work out4!,multiply4by3!to get24here3! = 1*2*3 = 6

To work out3!, multiply3by2!to get6here2! = 1*2 = 2

To work out2!, multiply2by1!to get2here1! = 1

To work out1!, multiply1by0!to get1here0! = 1

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

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