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++
// 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 // 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 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
<?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 // 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
//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" ); } |
Yes
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