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 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 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
// 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"); }} |
Python3
# 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 # 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#
// 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// 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
//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");} |
Output
Yes
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