How to compute mod of a big number?

Given a big number ‘num’ represented as string and an integer x, find value of “num % x” or “num mod x”. Output is expected as an integer.

Examples :

Input:  num = "12316767678678",  a = 10
Output: num (mod a) ≡ 8

The idea is to process all digits one by one and use the property that xy (mod a) ≡ ((x (mod a) * y) (mod a)). Below is the implementation.

Thanks to utkarsh111 for suggesting the below solution.

C++

// C++ program to compute mod of a big number represented 
// as string 
#include<iostream> 
using namespace std; 
  
// Function to compute num (mod a) 
int mod(string num, int a) 
{ 
    // Initialize result 
    int res = 0; 
  
    // One by one process all digits of 'num' 
    for (int i = 0; i < num.length(); i++) 
         res = (res*10 + (int)num[i] - '0') %a; 
  
    return res; 
} 
  
// Driver program 
int main() 
{ 
    string num = "12316767678678"; 
    cout << mod(num, 10); 
    return 0; 
} 

Java

// Java program to compute mod of a big  
// number represented as string 
import java.io.*; 
  
class GFG { 
      
    // Function to compute num (mod a) 
    static int mod(String num, int a) 
    { 
          
        // Initialize result 
        int res = 0; 
  
        // One by one process all digits of 'num' 
        for (int i = 0; i < num.length(); i++) 
            res = (res * 10 + (int)num.charAt(i) 
                                     - '0') % a; 
  
        return res; 
    } 
  
    // Driver program 
    public static void main(String[] args) 
    { 
          
        String num = "12316767678678"; 
          
        System.out.println(mod(num, 10)); 
    } 
} 
  
// This code is contributed by vt_m. 

Python3

# program to compute mod of a big number 
# represented as string 
  
# Function to compute num (mod a) 
def mod(num, a): 
      
    # Initialize result 
    res = 0
  
    # One by one process all digits 
    # of 'num' 
    for i in range(0, len(num)): 
        res = (res * 10 + int(num[i])) % a; 
  
    return res 
  
# Driver program 
num = "12316767678678"; 
print(mod(num, 10)) 
  
# This code is contributed by Sam007 

C#

// C# program to compute mod of a big  
// number represented as string 
using System; 
  
public class GFG  
{ 
      
    // Function to compute num (mod a) 
    static int mod(String num, int a) 
    { 
          
        // Initialize result 
        int res = 0; 
  
        // One by one process all  
        // digits of 'num' 
        for (int i = 0; i < num.Length; i++) 
            res = (res * 10 + (int)num[i]-  
                   '0') % a; 
  
        return res; 
    } 
  
    // Driver code 
    public static void Main() 
    { 
        String num = "12316767678678"; 
          
        Console.WriteLine(mod(num, 10)); 
    } 
} 
  
// This code is contributed by Sam007 

PHP

<?php 
// PHP program to compute mod  
// of a big number represented  
// as string 
  
// Function to compute num (mod a) 
function mod($num, $a) 
{ 
    // Initialize result 
    $res = 0; 
  
    // One by one process  
    // all digits of 'num' 
    for ($i = 0; $i < $r = strlen($num); $i++) 
        $res = ($res * 10 +  
                $num[$i] - '0') % $a; 
  
    return $res; 
} 
  
// Driver Code 
$num = "12316767678678"; 
echo mod($num, 10); 
  
// This code is contributed by ajit 
?> 

Output :

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My Personal Notes

C++

Java

Python3

C#

PHP

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