Check if a large number is divisible by 4 or not

04 Jul, 2022
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 idea :
C++
Java
Python3
C#
PHP
Javascript
// 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 notbool 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    // divisible by 4.    int last = str[n - 1] - '0';    int second_last = str[n - 2] - '0';    return ((second_last * 10 + last) % 4 == 0);} // Driver codeint main(){    string str = "76952";       // Function call    check(str) ? cout << "Yes" : cout << "No ";    return 0;}
// Java program to find if a number is// divisible by 4 or notclass 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        // divisible by 4.        int last = str.charAt(n - 1) - '0';        int second_last = str.charAt(n - 2) - '0';        return ((second_last * 10 + last) % 4 == 0);    }     // Driver code    public static void main(String[] args)    {        String str = "76952";               // Function call        if (check(str))            System.out.println("Yes");        else            System.out.println("No");    }}
# 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    # divisible by 4.    last = (int)(st[n - 1])    second_last = (int)(st[n - 2])     return ((second_last * 10 + last) % 4 == 0)  # Driver codest = "76952" # Function callif(check(st)):    print("Yes")else:    print("No ") # This code is contributed by Nikita tiwari
// C# program to find if a number is// divisible by 4 or notusing 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 divisible by 4.        int last = str[n - 1] - '0';        int second_last = str[n - 2] - '0';         return ((second_last * 10 + last) % 4 == 0);    }     // Driver code    public static void Main()    {        String str = "76952";         // Function call        if (check(str))            Console.Write("Yes");        else            Console.Write("No");    }} // This code is Contributed by nitin mittal.
<?php// PHP program to find if a// number is divisible by// 4 or not // Function to find that// number divisible by// 4 or notfunction 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    // divisible by 4.    $last = $str[$n - 1] - '0';    $second_last = $str[$n - 2] - '0';    return (($second_last * 10 + $last) % 4 == 0);} // Driver code$str = "76952"; // Function call$x = check($str)? "Yes" : "No";echo($x); // This code is contributed by Ajit.?>
//Javascript program to check whether a string is divisible by 4 or not // function to check the divisibilityfunction check(str){       // checking the length for future reference      var n = str.length;       // if it is empty then directly returning false      if( n == 0)      {                   return false;      }        if( n == 1)      {           return ((str[0] -'0') % 4 == 0);      }      var lastNumber = str[n-1] -'0';      var lastSecondNUmber = str[n-2] -'0';      return ((lastSecondNUmber * 10  + lastNumber) % 4 == 0);   } // Driver codevar str="76952"; //checking the value by passing it into the function// Function callif(check(str)){  console.log("Yes");}else{  console.log("No");}
Yes
Time Complexity: O(1), as we are not using any loops for traversing.
Auxiliary Space: O(1), as we are not using any extra space. 
Method 2: Checking given number is divisible by 4 or not by using the modulo division operator “%”. 
Python3
Javascript
# Python code# To check whether the given number is divisible by 4 or not #inputn=1234567589333862# the above input can also be given as n=input() -> taking input from user# finding given number is divisible by 4 or notif int(n)%4==0:  print("Yes")else:  print("No")   # this code is contributed by gangarajula laxmi
<script>       // JavaScript code for the above approach       // To check whether the given number is divisible by 4 or not        //input       var n = 1234567589333862       // the above input can also be given as n=input() -> taking input from user       // finding given number is divisible by 4 or not       if (n % 4 == 0)           document.write("Yes")       else           document.write("No")    // This code is contributed by Potta Lokesh   </script>
No
Time Complexity: O(1), as we are not using any loops for traversing.
Auxiliary Space: O(1), as we are not using any extra space. 
Method 3: Use of inbuilt function Atoi() in C++.The atoi() function in C++ takes a string (which represents an integer) as an argument and returns its value of type int. So basically the function is used to convert a string argument to an integer.
Syntax:  
int atoi(const char str)
Parameters: The function accepts one parameter str which refers to the string argument that is needed to be converted into its integer equivalent.
Return Value: If str is a valid input, then the function returns the equivalent integer number for the passed string number. If no valid conversion takes place, then the function returns zero.
Implementation
C++
// C++ program to find if a number is divisible by// 4 or not#include <bits/stdc++.h>using namespace std; // Driver codeint main(){    char str[] = "76952";    int n = (sizeof(str) / sizeof(char))-1;    char ch[2];    if (n >= 2) {        ch[0] = str[n - 2];        ch[1] = str[n - 1];    }    else if (n == 1) {        ch[0] = 0;        ch[1] = str[0];    }     int x;    x = atoi(ch);    if (!(x % 4)) {        cout << "YES";    }    else {        cout << "NO";    }     return 0;} // This code is contributed by Aarti_Rathi
YES
Time Complexity: O(1), as we are not using any loops for traversing.
Auxiliary Space: O(1), as we are not using any extra space. 
Method 4: (Using substring function)
Use substring function to get the last two characters of the string.
Convert the string to integer
Check if it is divisible by 4 or not, using (number%4 == 0).
This approach is contributed by Abhijeet Kumar.
Below is the implementation of the above approach:
C++
Java
Python3
C#
Javascript
// 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 notbool check(string str){    // Get the length of the string    int n = str.length();     // Empty string    if (n == 0)        return false;    // stoi(string_variable) is used in C++    // to convert string to integer     // If there is single digit    if (n == 1)        return ((stoi(str)) % 4 == 0);     // getting last two characters using substring    str = str.substr(n - 2, 2);    // If number formed by last two digits is    // divisible by 4.    return ((stoi(str)) % 4 == 0);} // Driver codeint main(){    string str = "76952";     // Function call    check(str) ? cout << "Yes" : cout << "No ";    return 0;} // This code is contributed by Abhijeet Kumar(abhijeet19403)
// Java program to find if a number is// divisible by 4 or notclass IsDivisible {    // Function to find that number    // is divisible by 4 or not    static boolean check(String str)    {        // Get the length of the string        int n = str.length();         // Empty string        if (n == 0)            return false;        // Integer.parseInt(string_variable) is used in Java        // to convert string to integer         // If there is single digit        if (n == 1)            return ((Integer.parseInt(str)) % 4 == 0);         // getting last two characters using substring        str = str.substring(n - 2);        // If number formed by last two digits is        // divisible by 4.        return ((Integer.parseInt(str)) % 4 == 0);    }     // Driver code    public static void main(String[] args)    {        String str = "76952";         // Function call        if (check(str))            System.out.println("Yes");        else            System.out.println("No");    }}// This code is contributed by Abhijeet Kumar(abhijeet19403)
# Python 3 program to find# if a number is divisible# by 4 or not # Function to find that# number divisible by# 4 or notdef check(st):    n = len(st)     # Empty string    if (n == 0):        return False     # int(string_variable) is used in Python3    # to convert string to integer     # If there is single    # digit    if (n == 1):        return (int(st) % 4 == 0)     # slicing of strings is used in Python to function as substring    st = st[n-2:]    # If number formed by    # last two digits is    # divisible by 4.    return (int(st) % 4 == 0)  # Driver codest = "76952" # Function callif(check(st)):    print("Yes")else:    print("No ") # This code is contributed by Abhijeet Kumar(abhijeet19403)
// C# program to find if a number is// divisible by 4 or notusing 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;               // int.Parse(string_variable) is used in C#        // to convert string to integer               // If there is single digit        if (n == 1)            return (int.Parse(str) % 4 == 0);                   // getting last two characters using substring          str = str.Substring(n-2);        // If number formed by last two        // digits is divisible by 4.        return (int.Parse(str) % 4 == 0);    }     // Driver code    public static void Main()    {        String str = "76952";         // Function call        if (check(str))            Console.Write("Yes");        else            Console.Write("No");    }} // This code is Contributed by Abhijeet Kumar(abhijeet19403)
//Javascript program to check whether a string is divisible by 4 or not // function to check the divisibilityfunction check(str){       // checking the length for future reference      var n = str.length;       // if it is empty then directly returning false      if( n == 0)      {                   return false;      }              // parseInt(string_variable) is used in Javascript      // to convert string to integer      if( n == 1)      {           return (parseInt(str) % 4 == 0);      }             // getting last two characters using substring      str = str.substring(n-2);             // If number formed by last two digits is      // divisible by 4.      return (parseInt(str) % 4 == 0);   } // Driver codevar str="76952"; //checking the value by passing it into the function// Function callif(check(str)){  console.log("Yes");}else{  console.log("No");}// This code is contributed by Abhijeet Kumar(abhijeet19403)
Yes
Time Complexity: (1)
substring function takes O(n) time, where n is the length of the substring and as here n is equal to 2 thus the time complexity is constant.
Auxiliary Space: O(1) 
As constant extra space is used.
This article is contributed by Aarti_Rathi and DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
nitin mittal
jit_t
ManasChhabra2
bunnyram19
rohitsingh07052
laxmigangarajula03
sachinvinod1904
abhijeet19403
lokeshpotta20
divisibility
large-numbers
number-digits
Mathematical
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