# Divide two integers without using multiplication, division and mod operator

Given a two integers say a and b. Find the quotient after dividing a by b without using multiplication, division and mod operator.

Example:

```Input : a = 10, b = 3
Output : 3

Input : a = 43, b = -8
Output :  -5
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach : Keep subtracting the divisor from dividend until dividend becomes less than divisor. The dividend becomes the remainder, and the number of times subtraction is done becomes the quotient. Below is the implementation of above approach :

## C++

 `// C++ implementation to Divide two ` `// integers without using multiplication, ` `// division and mod operator ` `#include ` `using` `namespace` `std; ` ` `  `// Function to divide a by b and ` `// return floor value it ` `int` `divide(``int` `dividend, ``int` `divisor) { ` ` `  `  ``// Calculate sign of divisor i.e., ` `  ``// sign will be negative only iff ` `  ``// either one of them is negative ` `  ``// otherwise it will be positive ` `  ``int` `sign = ((dividend < 0) ^ (divisor < 0)) ? -1 : 1; ` ` `  `  ``// Update both divisor and ` `  ``// dividend positive ` `  ``dividend = ``abs``(dividend); ` `  ``divisor = ``abs``(divisor); ` ` `  `  ``// Initialize the quotient ` `  ``int` `quotient = 0; ` `  ``while` `(dividend >= divisor) { ` `    ``dividend -= divisor; ` `    ``++quotient; ` `  ``} ` ` `  `  ``return` `sign * quotient; ` `} ` ` `  `// Driver code ` `int` `main() { ` `  ``int` `a = 10, b = 3; ` `  ``cout << divide(a, b) << ``"\n"``; ` ` `  `  ``a = 43, b = -8; ` `  ``cout << divide(a, b); ` ` `  `  ``return` `0; ` `} `

## Java

 `/*Java implementation to Divide two ` `integers without using multiplication, ` `division and mod operator*/` ` `  `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `    ``// Function to divide a by b and ` `    ``// return floor value it ` `    ``static` `int` `divide(``int` `dividend, ``int` `divisor)  ` `    ``{ ` `         `  `        ``// Calculate sign of divisor i.e., ` `        ``// sign will be negative only iff ` `        ``// either one of them is negative ` `        ``// otherwise it will be positive ` `        ``int` `sign = ((dividend < ``0``) ^  ` `                   ``(divisor < ``0``)) ? -``1` `: ``1``; ` `     `  `        ``// Update both divisor and ` `        ``// dividend positive ` `        ``dividend = Math.abs(dividend); ` `        ``divisor = Math.abs(divisor); ` `     `  `        ``// Initialize the quotient ` `        ``int` `quotient = ``0``; ` `         `  `        ``while` `(dividend >= divisor) ` `        ``{ ` `            ``dividend -= divisor; ` `            ``++quotient; ` `        ``} ` `     `  `        ``return` `sign * quotient; ` `    ``}     ` `     `  `    ``public` `static` `void` `main (String[] args)  ` `    ``{ ` `        ``int` `a = ``10``; ` `        ``int` `b = ``3``; ` `         `  `        ``System.out.println(divide(a, b)); ` `         `  `        ``a = ``43``; ` `        ``b = -``8``; ` `         `  `        ``System.out.println(divide(a, b)); ` `    ``} ` `} ` ` `  `// This code is contributed by upendra singh bartwal. `

## Python3

 `# Python 3 implementation to Divide two ` `# integers without using multiplication, ` `# division and mod operator ` ` `  `# Function to divide a by b and ` `# return floor value it ` `def` `divide(dividend, divisor):  ` ` `  `    ``# Calculate sign of divisor i.e., ` `    ``# sign will be negative only iff ` `    ``# either one of them is negative ` `    ``# otherwise it will be positive ` `    ``sign ``=` `-``1` `if` `((dividend < ``0``) ^  (divisor < ``0``)) ``else` `1` `     `  `    ``# Update both divisor and ` `    ``# dividend positive ` `    ``dividend ``=` `abs``(dividend) ` `    ``divisor ``=` `abs``(divisor) ` `     `  `    ``# Initialize the quotient ` `    ``quotient ``=` `0` `    ``while` `(dividend >``=` `divisor):  ` `        ``dividend ``-``=` `divisor ` `        ``quotient ``+``=` `1` `     `  `     `  `    ``return` `sign ``*` `quotient ` ` `  ` `  `# Driver code ` `a ``=` `10` `b ``=` `3` `print``(divide(a, b)) ` `a ``=` `43` `b ``=` `-``8` `print``(divide(a, b)) ` ` `  `# This code is contributed by ` `# Smitha Dinesh Semwal `

## C#

 `// C# implementation to Divide two without  ` `// using multiplication, division and mod ` `// operator ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Function to divide a by b and ` `    ``// return floor value it ` `    ``static` `int` `divide(``int` `dividend, ``int` `divisor)  ` `    ``{ ` `         `  `        ``// Calculate sign of divisor i.e., ` `        ``// sign will be negative only iff ` `        ``// either one of them is negative ` `        ``// otherwise it will be positive ` `        ``int` `sign = ((dividend < 0) ^  ` `                ``(divisor < 0)) ? -1 : 1; ` `     `  `        ``// Update both divisor and ` `        ``// dividend positive ` `        ``dividend = Math.Abs(dividend); ` `        ``divisor = Math.Abs(divisor); ` `     `  `        ``// Initialize the quotient ` `        ``int` `quotient = 0; ` `         `  `        ``while` `(dividend >= divisor) ` `        ``{ ` `            ``dividend -= divisor; ` `            ``++quotient; ` `        ``} ` `     `  `        ``return` `sign * quotient; ` `    ``}  ` `     `  `    ``public` `static` `void` `Main ()  ` `    ``{ ` `         `  `        ``int` `a = 10; ` `        ``int` `b = 3; ` `        ``Console.WriteLine(divide(a, b)); ` `         `  `        ``a = 43; ` `        ``b = -8; ` `        ``Console.WriteLine(divide(a, b)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 `= ``\$divisor``) ` `    ``{ ` `        ``\$dividend` `-= ``\$divisor``; ` `        ``++``\$quotient``; ` `    ``} ` `     `  `    ``return` `\$sign` `* ``\$quotient``; ` `} ` ` `  `// Driver code ` `\$a` `= 10; ` `\$b` `= 3; ` `echo` `divide(``\$a``, ``\$b``).``"\n"``; ` ` `  `\$a` `= 43; ` `\$b` `= -8; ` `echo` `divide(``\$a``, ``\$b``); ` ` `  `// This code is contributed by Sam007 ` `?> `

Output :

```3
-5
```

Time complexity : O(a)
Auxiliary space : O(1)

Efficient Approach : Use bit manipulation in order to find the quotient. The divisor and dividend can be written as

dividend = quotient * divisor + remainder

As every number can be represented in base 2(0 or 1), represent the quotient in binary form by using shift operator as given below :

1. Determine the most significant bit in the quotient. This can easily be calculated by iterating on the bit position i from 31 to 1.
2. Find the first bit for which is less than dividend and keep updating the ith bit position for which it is true.
3. Add the result in temp variable for checking the next position such that (temp + (divisor << i) ) is less than dividend.
4. Return the final answer of quotient after updating with corresponding sign.

Below is the implementation of above approach :

## C++

 `// C++ implementation to Divide two ` `// integers without using multiplication, ` `// division and mod operator ` `#include ` `using` `namespace` `std; ` ` `  `// Function to divide a by b and ` `// return floor value it ` `int` `divide(``long` `long` `dividend, ``long` `long` `divisor) { ` ` `  `  ``// Calculate sign of divisor i.e., ` `  ``// sign will be negative only iff ` `  ``// either one of them is negative ` `  ``// otherwise it will be positive ` `  ``int` `sign = ((dividend < 0) ^ (divisor < 0)) ? -1 : 1; ` ` `  `  ``// remove sign of operands ` `  ``dividend = ``abs``(dividend); ` `  ``divisor = ``abs``(divisor); ` ` `  `  ``// Initialize the quotient ` `  ``long` `long` `quotient = 0, temp = 0; ` ` `  `  ``// test down from the highest bit and ` `  ``// accumulate the tentative value for ` `  ``// valid bit ` `  ``for` `(``int` `i = 31; i >= 0; --i) { ` ` `  `    ``if` `(temp + (divisor << i) <= dividend) { ` `      ``temp += divisor << i; ` `      ``quotient |= 1LL << i; ` `    ``} ` `  ``} ` ` `  `  ``return` `sign * quotient; ` `} ` ` `  `// Driver code ` `int` `main() { ` `  ``int` `a = 10, b = 3; ` `  ``cout << divide(a, b) << ``"\n"``; ` ` `  `  ``a = 43, b = -8; ` `  ``cout << divide(a, b); ` ` `  `  ``return` `0; ` `} `

## Java

 `// Java implementation to Divide  ` `// two integers without using  ` `// multiplication, division  ` `// and mod operator  ` `import` `java.io.*;  ` `import` `java.util.*;  ` ` `  `// Function to divide a by b  ` `// and return floor value it  ` `class` `GFG  ` `{  ` `public` `static` `long` `divide(``long` `dividend,  ` `                        ``long` `divisor)  ` `{  ` ` `  `// Calculate sign of divisor  ` `// i.e., sign will be negative  ` `// only iff either one of them  ` `// is negative otherwise it  ` `// will be positive  ` `long` `sign = ((dividend < ``0``) ^  ` `            ``(divisor < ``0``)) ? -``1` `: ``1``;  ` ` `  `// remove sign of operands  ` `dividend = Math.abs(dividend);  ` `divisor = Math.abs(divisor);  ` ` `  `// Initialize the quotient  ` `long` `quotient = ``0``, temp = ``0``;  ` ` `  `// test down from the highest  ` `// bit and accumulate the  ` `// tentative value for  ` `// valid bit  ` `// 1<<31 behaves incorrectly and gives Integer ` `// Min Value which should not be the case, instead  ` `  ``// 1L<<31 works correctly.  ` `for` `(``int` `i = ``31``; i >= ``0``; --i)  ` `{  ` ` `  `    ``if` `(temp + (divisor << i) <= dividend)  ` `    ``{  ` `        ``temp += divisor << i;  ` `        ``quotient |= 1L << i;  ` `    ``}  ` `}  ` ` `  `return` `(sign * quotient);  ` `}  ` ` `  `// Driver code  ` `public` `static` `void` `main(String args[])  ` `{  ` `int` `a = ``10``, b = ``3``;  ` `System.out.println(divide(a, b));  ` ` `  `int` `a1 = ``43``, b1 = -``8``;  ` `System.out.println(divide(a1, b1));  ` ` `  ` `  `}  ` `}  ` ` `  `// This code is contributed  ` `// by Akanksha Rai(Abby_akku)  `

## Python3

 `# Python3 implementation to  ` `# Divide two integers  ` `# without using multiplication, ` `# division and mod operator ` ` `  `# Function to divide a by  ` `# b and return floor value it ` `def` `divide(dividend, divisor): ` `     `  `    ``# Calculate sign of divisor  ` `    ``# i.e., sign will be negative ` `    ``# either one of them is negative ` `    ``# only iff otherwise it will be ` `    ``# positive ` `     `  `    ``sign ``=` `(``-``1` `if``((dividend < ``0``) ^  ` `                  ``(divisor < ``0``)) ``else` `1``); ` `     `  `    ``# remove sign of operands ` `    ``dividend ``=` `abs``(dividend); ` `    ``divisor ``=` `abs``(divisor); ` `     `  `    ``# Initialize ` `    ``# the quotient ` `    ``quotient ``=` `0``; ` `    ``temp ``=` `0``; ` `     `  `    ``# test down from the highest  ` `    ``# bit and accumulate the  ` `    ``# tentative value for valid bit ` `    ``for` `i ``in` `range``(``31``, ``-``1``, ``-``1``): ` `        ``if` `(temp ``+` `(divisor << i) <``=` `dividend): ` `            ``temp ``+``=` `divisor << i; ` `            ``quotient |``=` `1` `<< i; ` `     `  `    ``return` `sign ``*` `quotient; ` ` `  `# Driver code ` `a ``=` `10``; ` `b ``=` `3``; ` `print``(divide(a, b)); ` ` `  `a ``=` `43``; ` `b ``=` `-``8``; ` `print``(divide(a, b)); ` ` `  `# This code is contributed by mits `

## C#

 `// C# implementation to Divide ` `// two integers without using  ` `// multiplication, division  ` `// and mod operator ` `using` `System; ` ` `  `// Function to divide a by b ` `// and return floor value it ` `class` `GFG ` `{ ` `public` `static` `long` `divide(``long` `dividend,  ` `                          ``long` `divisor)  ` `{ ` ` `  `// Calculate sign of divisor  ` `// i.e., sign will be negative  ` `// only iff either one of them  ` `// is negative otherwise it  ` `// will be positive ` `long` `sign = ((dividend < 0) ^  ` `             ``(divisor < 0)) ? -1 : 1; ` ` `  `// remove sign of operands ` `dividend = Math.Abs(dividend); ` `divisor = Math.Abs(divisor); ` ` `  `// Initialize the quotient ` `long` `quotient = 0, temp = 0; ` ` `  `// test down from the highest  ` `// bit and accumulate the  ` `// tentative value for ` `// valid bit ` `for` `(``int` `i = 31; i >= 0; --i)  ` `{ ` ` `  `    ``if` `(temp + (divisor << i) <= dividend)  ` `    ``{ ` `        ``temp += divisor << i; ` `        ``quotient |= 1LL << i; ` `    ``} ` `} ` ` `  `return` `(sign * quotient); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main()  ` `{ ` `int` `a = 10, b = 3; ` `Console.WriteLine(divide(a, b)); ` ` `  `int` `a1 = 43, b1 = -8; ` `Console.WriteLine(divide(a1, b1)); ` ` `  `} ` `} ` ` `  `// This code is contributed by mits `

## PHP

 `= 0; --``\$i``)  ` `{ ` ` `  `    ``if` `(``\$temp` `+ (``\$divisor` `<< ``\$i``) <= ``\$dividend``)  ` `    ``{ ` `        ``\$temp` `+= ``\$divisor` `<< ``\$i``; ` `        ``\$quotient` `|= (double)(1) << ``\$i``; ` `    ``} ` `} ` ` `  `return` `\$sign` `* ``\$quotient``; ` `} ` ` `  `// Driver code ` `\$a` `= 10; ` `\$b` `= 3; ` `echo` `divide(``\$a``, ``\$b``). ``"\n"``; ` ` `  `\$a` `= 43; ` `\$b` `= -8; ` `echo` `divide(``\$a``, ``\$b``); ` ` `  `// This code is contributed by mits ` `?> `

Output :

```3
-5
```

Time complexity : O(log(a))
Auxiliary space : O(1)

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