Divide large number represented as string

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Given a large number (represented as a string) which has to divide by another number (represented as int data type). The large number can be very large which does not even fit in long long in C++. The task is to find the division of these numbers.

Examples:

Input : number  = 1260257
        divisor = 37
Output : 34061
(See below diagram)

Input : number  = 12313413534672234
        divisor = 754
Output : 16330787181262

Input : number  = 1248163264128256512
        divisor = 125
Output : 9985306113026052

We have already discussed Multiply Large Numbers represented as Strings.
We use basic school mathematics as shown in below example.

division

As the dividend and result can be very large we store them in string. We first take digits which are divisible by number. After this take each digit and store result in string.

Implementation:

C++

// C++ program to implement division with large 
// number 
#include <bits/stdc++.h> 
using namespace std; 
  
// A function to perform division of large numbers 
string longDivision(string number, int divisor) 
{ 
    // As result can be very large store it in string 
    string ans; 
  
    // Find prefix of number that is larger 
    // than divisor. 
    int idx = 0; 
    int temp = number[idx] - '0'; 
    while (temp < divisor) 
        temp = temp * 10 + (number[++idx] - '0'); 
  
    // Repeatedly divide divisor with temp. After 
    // every division, update temp to include one 
    // more digit. 
    while (number.size() > idx) { 
        // Store result in answer i.e. temp / divisor 
        ans += (temp / divisor) + '0'; 
  
        // Take next digit of number 
        temp = (temp % divisor) * 10 + number[++idx] - '0'; 
    } 
  
    // If divisor is greater than number 
    if (ans.length() == 0) 
        return "0"; 
  
    // else return ans 
    return ans; 
} 
  
// Driver program to test longDivision() 
int main() 
{ 
    string number = "1248163264128256512"; 
    int divisor = 125; 
    cout << longDivision(number, divisor); 
    return 0; 
} 

Java

// Java program to implement division 
// with large number 
import java.io.*; 
public class GFG { 
    public static String longDivision( 
        String number, 
        int divisor) 
    { 
  
        // As result can be very 
        // large store it in string 
        // but since we need to modify 
        // it very often so using 
        // string builder 
        StringBuilder result 
            = new StringBuilder(); 
  
        // We will be iterating 
        // the dividend so converting 
        // it to char array 
        char[] dividend 
            = number.toCharArray(); 
  
        // Initially the carry 
        // would be zero 
        int carry = 0; 
  
        // Iterate the dividend 
        for ( 
            int i = 0; 
            i < dividend.length; i++) { 
            // Prepare the number to 
            // be divided 
            int x 
                = carry * 10
                  + Character.getNumericValue( 
                        dividend[i]); 
  
            // Append the result with 
            // partial quotient 
            result.append(x / divisor); 
  
            // Prepare the carry for 
            // the next Iteration 
            carry = x % divisor; 
        } 
  
        // Remove any leading zeros 
        for ( 
            int i = 0; 
            i < result.length(); i++) { 
            if ( 
                result.charAt(i) != '0') { 
                // Return the result 
                return result.substring(i); 
            } 
        } 
        // Return empty string 
        // if number is empty 
        return ""; 
    } 
  
    // Driver code 
    public static void main( 
        String[] args) 
    { 
        String number 
            = "1248163264128256512"; 
        int divisor = 125; 
        System.out.println( 
            longDivision( 
                number, divisor)); 
    } 
} 
  
// This code is contributed by Saurabh321Gupta. 

Python3

# Python3 program to implement division  
# with large number  
import math 
  
# A function to perform division of  
# large numbers  
def longDivision(number, divisor):  
  
    # As result can be very large  
    # store it in string  
    ans = "";  
      
    # Find prefix of number that  
    # is larger than divisor.  
    idx = 0;  
    temp = ord(number[idx]) - ord('0'); 
    while (temp < divisor): 
        temp = (temp * 10 + ord(number[idx + 1]) -
                            ord('0')); 
        idx += 1; 
      
    idx += 1; 
  
    # Repeatedly divide divisor with temp.  
    # After every division, update temp to  
    # include one more digit.  
    while ((len(number)) > idx):  
          
        # Store result in answer i.e. temp / divisor  
        ans += chr(math.floor(temp // divisor) + ord('0'));  
          
        # Take next digit of number 
        temp = ((temp % divisor) * 10 + ord(number[idx]) -
                                        ord('0')); 
        idx += 1; 
  
    ans += chr(math.floor(temp // divisor) + ord('0')); 
      
    # If divisor is greater than number  
    if (len(ans) == 0):  
        return "0";  
      
    # else return ans  
    return ans;  
  
# Driver Code 
number = "1248163264128256512";  
divisor = 125;  
print(longDivision(number, divisor));  
      
# This code is contributed by mits 

C#

// C# program to implement division 
// with large number 
using System; 
  
class GFG { 
  
    // A function to perform division of large numbers 
    static string longDivision(string number, int divisor) 
    { 
        // As result can be very large store it in string 
        string ans = ""; 
  
        // Find prefix of number that is larger 
        // than divisor. 
        int idx = 0; 
        int temp = (int)(number[idx] - '0'); 
        while (temp < divisor) { 
            temp = temp * 10 + (int)(number[idx + 1] - '0'); 
            idx++; 
        } 
        ++idx; 
  
        // Repeatedly divide divisor with temp. After 
        // every division, update temp to include one 
        // more digit. 
        while (number.Length > idx) { 
            // Store result in answer i.e. temp / divisor 
            ans += (char)(temp / divisor + '0'); 
  
            // Take next digit of number 
            temp = (temp % divisor) * 10 + (int)(number[idx] - '0'); 
            idx++; 
        } 
        ans += (char)(temp / divisor + '0'); 
  
        // If divisor is greater than number 
        if (ans.Length == 0) 
            return "0"; 
  
        // else return ans 
        return ans; 
    } 
  
    // Driver code 
    static void Main() 
    { 
        string number = "1248163264128256512"; 
        int divisor = 125; 
        Console.WriteLine(longDivision(number, divisor)); 
    } 
} 
  
// This code is contributed by mits 

PHP

<?php 
// PHP program to implement division  
// with large number  
  
// A function to perform division of 
// large numbers  
function longDivision($number, $divisor)  
{  
    // As result can be very large  
    // store it in string  
    $ans = "";  
      
    // Find prefix of number that is 
    // larger than divisor.  
    $idx = 0;  
    $temp = ord($number[$idx]) - 48;  
    while ($temp < $divisor)  
        $temp = $temp * 10 +  
            ord($number[++$idx]) - 48;  
      
    // Repeatedly divide divisor with temp. 
    // After every division, update temp to  
    // include one more digit. 
    ++$idx; 
    while (strlen($number) > $idx)  
    {  
        // Store result in answer i.e. temp / divisor  
        $ans .= chr((int)($temp / $divisor) + 48);  
          
        // Take next digit of number  
        $temp = ($temp % $divisor) * 10 +  
             ord($number[$idx]) - 48; 
        ++$idx; 
    }  
    $ans .= chr((int)($temp / $divisor) + 48); 
      
    // If divisor is greater than number  
    if (strlen($ans) == 0)  
        return "0";  
      
    // else return ans  
    return $ans;  
}  
  
// Driver Code 
$number = "1248163264128256512";  
$divisor = 125;  
print(longDivision($number, $divisor));  
  
// This code is contributed by mits 
?> 

Javascript

<script> 
  
// Javascript program to implement division 
// with large number 
      
      
    function longDivision(number,divisor) 
    { 
        // As result can be very 
        // large store it in string 
        // but since we need to modify 
        // it very often so using 
        // string builder 
        let ans=""; 
    
        // We will be iterating 
        // the dividend so converting 
        // it to char array 
    
        // Initially the carry 
        // would be zero 
        let idx = 0; 
          let temp=number[idx]-'0'; 
        while (temp < divisor) 
        { 
            temp = (temp * 10 +  
            (number[idx + 1]).charCodeAt(0) - 
                   ('0').charCodeAt(0)); 
            idx += 1; 
        } 
        idx += 1; 
          
        while(number.length>idx) 
        { 
            // Store result in answer i.e. temp / divisor  
            ans += String.fromCharCode 
            (Math.floor(temp / divisor) + 
            ('0').charCodeAt(0));  
            
            // Take next digit of number 
            temp = ((temp % divisor) * 10 +  
            (number[idx]).charCodeAt(0) - 
                  ('0').charCodeAt(0)); 
            idx += 1; 
        } 
          
        ans += String.fromCharCode 
        (Math.floor(temp / divisor) +  
        ('0').charCodeAt(0)); 
          
        //If divisor is greater than number  
        if(ans.length==0) 
            return "0"; 
        //else return ans  
        return ans; 
    } 
      
    // Driver Code 
    let number = "1248163264128256512"; 
    let divisor = 125; 
    document.write(longDivision( 
                number, divisor)); 
      
    // This code is contributed  
    // by avanitrachhadiya2155 
      
</script>

Output

9985306113026052

Time Complexity: O(n²!), where n denoting length of string.
Auxiliary Space: O(n).

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Last Updated : 15 Sep, 2023