# Factorial of a number without using multiplication

Given a positive number N, the task is to calculate the factorial of N without using the multiplication operator.

Examples:

Input: N = 5
Output:
120
Explanation:
5*4*3*2*1=120

Input: N = 7
Output:
5040

Observation:

```A*B=A+A+A+A...B times.

This observation can be used as follows:
5!=5*4*3*2*1
=(5+5+5+5)*3*2*1
=(20+20+20)*2*1
=60+60
=120```

Approach 1: The problem can be solved using the concept of nested loops. Instead of using the multiplication operator, the answer can be manually calculated by using another loop. Follow the steps below to solve the problem:

1. Initialize a variable ans to N.
2. Iterate from N-1 to 1, using the variable i, and do the following:
• Initialize a variable sum to 0.
• Iterate from 0 to i-1, using the variable j, and add ans to sum
• Add sum to ans.
3. Print ans.

Below is the implementation of the above approach

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to calculate factorial of the number``// without using multiplication operator``int` `factorialWithoutMul(``int` `N)``{``    ``// variable to store the final factorial``    ``int` `ans = N;` `    ``// Outer loop``    ``for` `(``int` `i = N - 1; i > 0; i--) {``        ``int` `sum = 0;` `        ``// Inner loop``        ``for` `(``int` `j = 0; j < i; j++)``            ``sum += ans;``        ``ans = sum;``    ``}``    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``// Input``    ``int` `N = 5;` `    ``// Function calling``    ``cout << factorialWithoutMul(N) << endl;``    ``return` `0;``}`

## Java

 `// Java program for the above approach` `import` `java.io.*;` `class` `GFG {``    ``// Function to calculate factorial of the number``    ``// without using multiplication operator``    ``public` `static` `int` `factorialWithoutMul(``int` `N)``    ``{``        ``// variable to store the final factorial``        ``int` `ans = N;` `        ``// Outer loop``        ``for` `(``int` `i = N - ``1``; i > ``0``; i--) {``            ``int` `sum = ``0``;` `            ``// Inner loop``            ``for` `(``int` `j = ``0``; j < i; j++)``                ``sum += ans;``            ``ans = sum;``        ``}``        ``return` `ans;``    ``}``    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `N = ``5``;` `        ``// Function calling``        ``System.out.println(factorialWithoutMul(N));``        ``// This code is contributed by Potta Lokesh``    ``}``}`

## Python3

 `# Python3 program for the above approach` `# Function to calculate factorial of the number``# without using multiplication operator`  `def` `factorialWithoutMul(N):` `    ``# Variable to store the final factorial``    ``ans ``=` `N` `    ``# Outer loop``    ``i ``=` `N ``-` `1` `    ``while` `(i > ``0``):``        ``sum` `=` `0` `        ``# Inner loop``        ``for` `j ``in` `range``(i):``            ``sum` `+``=` `ans` `        ``ans ``=` `sum``        ``i ``-``=` `1` `    ``return` `ans`  `# Driver code``if` `__name__ ``=``=` `'__main__'``:` `    ``# Input``    ``N ``=` `5` `    ``# Function calling``    ``print``(factorialWithoutMul(N))` `# This code is contributed by SURENDRA_GANGWAR`

## C#

 `// C# program for the above approach``using` `System;``using` `System.Collections.Generic;` `class` `GFG {` `    ``// Function to calculate factorial of the number``    ``// without using multiplication operator``    ``static` `int` `factorialWithoutMul(``int` `N)``    ``{` `        ``// Variable to store the final factorial``        ``int` `ans = N;` `        ``// Outer loop``        ``for` `(``int` `i = N - 1; i > 0; i--) {``            ``int` `sum = 0;` `            ``// Inner loop``            ``for` `(``int` `j = 0; j < i; j++)``                ``sum += ans;` `            ``ans = sum;``        ``}``        ``return` `ans;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{` `        ``// Input``        ``int` `N = 5;` `        ``// Function calling``        ``Console.Write(factorialWithoutMul(N));``    ``}``}` `// This code is contributed by SURENDRA_GANGWAR`

## Javascript

 ``

Output
`120`

Time Complexity: O(N2)
Auxiliary Space: O(1)

Approach 2: The problem can be solved by dividing with the reciprocal of the next number instead of multiplying it. In algebra, ab also means a / (1/b). We will be using the same concept to find the factorial of a number without using asterisk. Follow the steps below to solve the problem:

1. Take a variable of integer type (here: n) which would store the value of which we’re finding the factorial.
2. Initialize a variable (here: p) which would serve to be the factorial of n.
3. Start iterating from n to 1. In each step, set the value of p to be the same as that of p divided by the reciprocal of iterator (here: i).
4. Print p.

Below is the implementation of the above approach in java:

## C++

 `// C++ code for the above approach` `#include ``using` `namespace` `std;` `int` `factorial(``int` `n)``{``  ` `    ``// Function to find the factorial of (n) without``    ``// multiplying.``    ``int` `p = 1;``    ``for` `(``int` `i = n; i >= 1; i--) ``    ``{``      ` `        ``// Loop to calculate the factorial of (n).``        ``p = p / (1.0 / i);``    ``}``  ` `    ``// Returning the factorial of (n) stored in (p).``    ``return` `p;``}` `int` `main()``{` `    ``int` `n = 5;``    ``// Printing the factorial of (n).``    ``cout << factorial(n) << endl;``    ``return` `0;``}` `// This code is contributed by lokesh.`

## Java

 `public` `class` `Factorial {``    ``int` `factorial(``int` `n)``    ``{ ``// Function to find the factorial of (n) without``      ``// multiplying.``        ``int` `p = ``1``;``        ``for` `(``int` `i = n; i >= ``1``;``             ``i--) { ``// Loop to calculate the factorial of``                    ``// (n).``            ``p = (``int``)(p / (``1.0` `/ i));``        ``}``        ``return` `p; ``// Returning the factorial of (n) stored``                  ``// in (p).``    ``}``    ``public` `static` `void` `main(String[] Args)``    ``{``        ``Factorial fact``            ``= ``new` `Factorial(); ``// Creating an instance of``                               ``// Factorial class.``        ``int` `n = ``5``;``        ``System.out.println(fact.factorial(``            ``n)); ``// Printing the factorial of (n).``    ``}``}`

## Python3

 `# Python3 code for the above approach``def` `factorial(n):``    ``# Function to find the factorial of (n) without multiplying.``    ``p ``=` `1``    ``for` `i ``in` `range``(n, ``0``, ``-``1``):``      ` `        ``# Loop to calculate the factorial of (n).``        ``p ``=` `p ``/` `(``1.0` `/` `i)` `    ``# Returning the factorial of (n) stored in (p).``    ``return` `p` `# Driver code``n ``=` `5` `# Printing the factorial of (n).``print``(factorial(n))` `#  This code is contributed by phasing17.`

## C#

 `// C# code for the above approach``using` `System;` `public` `class` `Factorial {` `  ``int` `factorial(``int` `n)``  ``{``    ` `    ``// Function to find the factorial of (n) without``    ``// multiplying.``    ``int` `p = 1;``    ``for` `(``int` `i = n; i >= 1; i--)``    ``{``      ` `      ``// Loop to calculate the factorial of (n).``      ``p = (``int``)(p / (1.0 / i));``    ``}``    ` `    ``// Returning the factorial of (n) stored in (p).``    ``return` `p;``  ``}` `  ``static` `public` `void` `Main()``  ``{` `    ``Factorial fact``      ``= ``new` `Factorial(); ``// Creating an instance of``    ``// Factorial class.``    ``int` `n = 5;``    ``Console.WriteLine(fact.factorial(``      ``n)); ``// Printing the factorial of (n).``  ``}``}` `// This code is contributed by lokeshmvs21.`

## Javascript

 `// JavaScript code for the above approach` `function` `factorial(n)``{``  ` `    ``// Function to find the factorial of (n) without``    ``// multiplying.``    ``let p = 1;``    ``for` `(let i = n; i >= 1; i--) ``    ``{``      ` `        ``// Loop to calculate the factorial of (n).``        ``p = p / (1.0 / i);``    ``}``  ` `    ``// Returning the factorial of (n) stored in (p).``    ``return` `p;``}` `    ``let n = 5;``    ` `    ``// Printing the factorial of (n).``    ``console.log(factorial(n))` `// This code is contributed by poojaagarwal2.`

Output
`120`

Time Complexity: O(N)

Auxiliary Space: O(1)

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