Check if a large number is divisible by 4 or not

Given a number, the task is to check if a number is divisible by 4 or not. The input number may be large and it may not be possible to store even if we use long long int.

Examples:

Input : n = 1124
Output : Yes

Input  : n = 1234567589333862
Output : No

Input  : n = 363588395960667043875487
Output : No



Since input number may be very large, we cannot use n % 4 to check if a number is divisible by 4 or not, especially in languages like C/C++. The idea is based on following fact.

A number is divisible by 4 if number formed by last two digits of it is divisible by 4.

Illustration:

For example, let us consider 76952 
Number formed by last two digits = 52
Since 52 is divisible by 4, answer is YES.

How does this work?

Let us consider 76952, we can write it as
76942 = 7*10000 + 6*1000 + 9*100 + 5*10 + 2

The proof is based on below observation:
Remainder of 10i divided by 4 is 0 if i greater 
than or equal to two. Note than 100, 1000,
... etc lead to remainder 0 when divided by 4.

So remainder of "7*10000 + 6*1000 + 9*100 + 
5*10 + 2" divided by 4 is equivalent to remainder 
of following : 
0 + 0 + 0 + 5*10 + 2 = 52
Therefore we can say that the whole number is 
divisible by 4 if 52 is divisible by 4.

Below is implementation of above fact :

C++

// C++ program to find if a number is divisible by
// 4 or not
#include<bits/stdc++.h>
using namespace std;
  
// Function to find that number divisible by
// 4 or not
bool check(string str)
{
    int n = str.length();
  
    // Empty string
    if (n == 0)
       return false;
  
    // If there is single digit
    if (n == 1)
       return ((str[0]-'0')%4 == 0);
  
    // If number formed by last two digits is
    // divisble by 4.
    int last = str[n-1] - '0';
    int second_last = str[n-2] - '0';
    return ((second_last*10 + last) % 4 == 0);
}
  
// Driver code
int main()
{
    string str = "76952";
    check(str)?  cout << "Yes" : cout << "No ";
    return 0;
}

Java

// Java program to find if a number is
// divisible by 4 or not
class IsDivisible
{
    // Function to find that number 
    // is divisible by 4 or not
    static boolean check(String str)
    {
        int n = str.length();
       
        // Empty string
        if (n == 0)
           return false;
       
        // If there is single digit
        if (n == 1)
           return ((str.charAt(0)-'0')%4 == 0);
       
        // If number formed by last two digits is
        // divisble by 4.
        int last = str.charAt(n-1) - '0';
        int second_last = str.charAt(n-2) - '0';
        return ((second_last*10 + last) % 4 == 0);
    }
  
    // main function
    public static void main (String[] args) 
    {
        String str = "76952";
        if(check(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }

Python3

# Python 3 program to find
# if a number is divisible
# by 4 or not
  
# Function to find that 
# number divisible by 
# 4 or not
def check(st) :
    n = len(st)
  
    # Empty string
    if (n == 0) :
        return False
  
    # If there is single 
    # digit
    if (n == 1) :
        return ((st[0] - '0') % 4 == 0)
  
    # If number formed by
    # last two digits is
    # divisble by 4.
    last = (int)(st[n - 1])
    second_last = (int)(st[n - 2])
      
    return ((second_last * 10 + last) % 4 == 0)
  
  
# Driver code
st = "76952"
if(check(st)) :
    print("Yes")
else
    print("No ")
      
# This code is contributed by Nikita tiwari

C#

// C# program to find if a number is
// divisible by 4 or not
using System;
  
class GFG {
      
    // Function to find that number 
    // is divisible by 4 or not
    static bool check(String str)
    {
        int n = str.Length;
      
        // Empty string
        if (n == 0)
            return false;
      
        // If there is single digit
        if (n == 1)
            return ((str[0] - '0') % 4 == 0);
      
        // If number formed by last two
        // digits is divisble by 4.
        int last = str[n-1] - '0';
        int second_last = str[n-2] - '0';
          
        return ((second_last*10 + last)
                                % 4 == 0);
    }
  
    // main function
    public static void Main () 
    {
        String str = "76952";
          
        if(check(str))
            Console.Write("Yes");
        else
            Console.Write("No");
    }
}
  
// This code is Contributed by nitin mittal.

PHP

<?php
// PHP program to find if a
// number is divisible by
// 4 or not
  
// Function to find that 
// number divisible by
// 4 or not
function check($str)
{
    $n = strlen($str);
  
    // Empty string
    if ($n == 0)
        return false;
  
    // If there is single digit
    if ($n == 1)
        return (($str[0] - '0') % 4 == 0);
  
    // If number formed by 
    // last two digits is
    // divisble by 4.
    $last = $str[$n - 1] - '0';
    $second_last = $str[$n - 2] - '0';
    return (($second_last * 10 + $last) % 4 == 0);
}
  
// Driver code
$str = "76952";
$x = check($str)? "Yes" : "No";
echo($x);
  
// This code is contributed by Ajit.
?>


Output:

Yes

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Improved By : nitin mittal, jit_t