Open in App
Not now

# Check if a large number is divisible by 4 or not

• Difficulty Level : Easy
• Last Updated : 08 Feb, 2023

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```
Recommended Practice

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++

 `// C++ program to find if a number is divisible by` `// 4 or not` `#include ` `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` `    ``// 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` `int` `main()` `{` `    ``string str = ``"76952"``;` `  `  `    ``// Function call` `    ``check(str) ? cout << ``"Yes"` `: cout << ``"No "``;` `    ``return` `0;` `}`

## Java

 `// Java program to find if a number is` `// divisible by 4 or not` `import` `java.util.*;` `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` `        ``// 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"``);` `    ``}` `}`

## 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` `    ``# divisible by 4.` `    ``last ``=` `(``int``)(st[n ``-` `1``])` `    ``second_last ``=` `(``int``)(st[n ``-` `2``])`   `    ``return` `((second_last ``*` `10` `+` `last) ``%` `4` `=``=` `0``)`     `# Driver code` `st ``=` `"76952"`   `# Function call` `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 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

 ``

## Javascript

 `//Javascript program to check whether a string is divisible by 4 or not`   `// function to check the divisibility` `function` `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 code` `var` `str=``"76952"``;`   `//checking the value by passing it into the function` `// Function call` `if``(check(str)){` `  ``console.log(``"Yes"``);` `}` `else``{` `  ``console.log(``"No"``);` `}`

Output

`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 “%”.

## C++

 `#include ` `using` `namespace` `std;` `int` `main()` `{` `    ``// input` `    ``long` `long` `int` `n = 1234567589333862;` `     `  `    ``// finding given number is divisible by 4 or not` `    ``if` `(n % 4 == 0)` `    ``{` `        ``cout << ``"Yes"``;` `    ``}` `    ``else` `    ``{` `        ``cout << ``"No"``;` `    ``}` `   `  `    ``return` `0;` `}`   `// This code is contributed by satwik4409.`

## Java

 `/*package whatever //do not write package name here */` `import` `java.io.*;`   `class` `GFG {` `    ``public` `static` `void` `main (String[] args) {` `      `  `      ``// input` `        ``long` `n=123456758933l;` `         `  `        ``// finding given number is divisible by 4 or not` `        ``if` `(n % ``4` `== ``0``)` `        ``{` `            ``System.out.println(``"Yes"``);` `        ``}` `        ``else` `        ``{` `            ``System.out.println(``"No"``);` `        ``}  ` `      `  `       `  `    ``}` `}`   `// This code is contributed by laxmigangarajula03`

## Python3

 `# Python code ` `# To check whether the given number is divisible by 4 or not`   `#input ` `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` `int``(n)``%``4``=``=``0``:` `  ``print``(``"Yes"``) ` `else``: ` `  ``print``(``"No"``)`   `  ``# this code is contributed by gangarajula laxmi`

## C#

 `using` `System;` `public` `class` `GFG{`   `    ``static` `public` `void` `Main (){`   `       ``// input` `        ``long` `n=1234567589333862;` `         `  `        ``// finding given number is divisible by 4 or not` `        ``if` `(n % 4 == 0)` `        ``{` `            ``Console.Write(``"Yes"``);` `        ``}` `        ``else` `        ``{` `            ``Console.Write(``"No"``);` `        ``}  ` `      `  `    ``}` `}`   `// This code is contributed by laxmigangarajula03`

## PHP

 ``

## Javascript

 ``

Output

`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 ` `using` `namespace` `std;`   `// Driver code` `int` `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`

## Java

 `// Java program to find if a number is divisible by` `// 4 or not` `import` `java.util.*;`   `class` `GFG` `{` `  `  `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``String str = ``"76952"``;` `        ``int` `n = str.length();`   `        ``char``[] ch = ``new` `char``[``2``];` `        ``if` `(n >= ``2``) {` `            ``ch[``0``] = str.charAt(n - ``2``);` `            ``ch[``1``] = str.charAt(n - ``1``);` `        ``}` `        ``else` `if` `(n == ``1``) {` `            ``ch[``0``] = ``'0'``;` `            ``ch[``1``] = str.charAt(``0``);` `        ``}`   `        ``int` `x = (ch[``0``] - ``'0'``) * ``10` `+ (ch[``1``] - ``'0'``);` `        ``if` `((x % ``4``) == ``0``) {` `            ``System.out.println(``"YES"``);` `        ``}` `        ``else` `{` `            ``System.out.println(``"NO"``);` `        ``}` `    ``}` `}`   `// This code is contributed by phasing17`

## Python3

 `# Python3 program to find if a number is divisible by` `# 4 or not`   `# Driver code` `str` `=` `"76952"``;` `n ``=` `len``(``str``);` `ch ``=` `["``", "``"]`   `if` `(n >``=` `2``):` `    ``ch[``0``] ``=` `str``[n ``-` `2``]` `    ``ch[``1``] ``=` `str``[n ``-` `1``]`   `elif` `(n ``=``=` `1``):` `    ``ch[``0``] ``=` `'0'``;` `    ``ch[``1``] ``=` `str``[``0``];`   `x ``=` `int``("".join(ch));` `if` `(x ``%` `4` `=``=` `0``):` `    ``print``(``"YES"``);`   `else``:` `    ``print``(``"NO"``);`     `# This code is contributed by phasing17`

## C#

 `// C# program to find if a number is divisible by` `// 4 or not` `using` `System;`   `class` `GFG {` `  ``// Driver code` `  ``public` `static` `void` `Main(``string``[] args)` `  ``{` `    ``string` `str = ``"76952"``;` `    ``int` `n = str.Length;` `    ``char``[] ch = ``new` `char``[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 = (ch[0] - ``'0'``) * 10 + (ch[1] - ``'0'``);` `    ``if` `((x % 4) == 0) {` `      ``Console.WriteLine(``"YES"``);` `    ``}` `    ``else` `{` `      ``Console.WriteLine(``"NO"``);` `    ``}` `  ``}` `}`   `// This code is contributed by phasing17`

## Javascript

 `// JavaScript program to find if a number is divisible by` `// 4 or not`   `// Driver code` `let str = ``"76952"``;` `let n = str.length;` `let ch = ``new` `Array(2);`   `if` `(n >= 2) {` `    ``ch[0] = str.charAt(n - 2);` `    ``ch[1] = str.charAt(n - 1);` `}`   `else` `if` `(n == 1) {` `    ``ch[0] = ``'0'``;` `    ``ch[1] = str.charAt(0);` `}`   `let x;` `x = parseInt(ch.join(``""``));` `if` `(x % 4 == 0) {` `    ``console.log(``"YES"``);` `}` `else` `{` `    ``console.log(``"NO"``);` `}`   `// This code is contributed by phasing17`

Output

`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++

 `// C++ program to find if a number is divisible by` `// 4 or not` `#include ` `using` `namespace` `std;`   `// Function to find that number divisible by` `// 4 or not` `bool` `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 code` `int` `main()` `{` `    ``string str = ``"76952"``;`   `    ``// Function call` `    ``check(str) ? cout << ``"Yes"` `: cout << ``"No "``;` `    ``return` `0;` `}`   `// This code is contributed by Abhijeet Kumar(abhijeet19403)`

## Java

 `// Java program to find if a number is` `// divisible by 4 or not` `import` `java.util.*;` `class` `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)`

## 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`   `    ``# 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 code` `st ``=` `"76952"`   `# Function call` `if``(check(st)):` `    ``print``(``"Yes"``)` `else``:` `    ``print``(``"No "``)`   `# This code is contributed by Abhijeet Kumar(abhijeet19403)`

## 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``;` `      `  `        ``// 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

 `//Javascript program to check whether a string is divisible by 4 or not`   `// function to check the divisibility` `function` `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 code` `var` `str=``"76952"``;`   `//checking the value by passing it into the function` `// Function call` `if``(check(str)){` `  ``console.log(``"Yes"``);` `}` `else``{` `  ``console.log(``"No"``);` `}` `// This code is contributed by Abhijeet Kumar(abhijeet19403)`

Output

`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.

My Personal Notes arrow_drop_up
Related Articles