Check if a large number is divisible by 8 or not

Given a number, the task is to check if a number is divisible by 8 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 = 1128
Output : Yes

Input : n = 1124
Output : No

Input  : n = 363588395960667043875487
Output : No



Since input number may be very large, we cannot use n % 8 to check if a number is divisible by 8 or not, especially in languages like C/C++. The idea is based on following fact.

A number is divisible by 8 if number formed by last three digits of it is divisible by 8.

Illustration:

For example, let us consider 76952 
Number formed by last three digits = 952
Since 952 is divisible by 8, 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 8 is 0 if i greater 
than or equal to three. Note than 10000, 
1000,... etc lead to remainder 0 when divided by 8.

So remainder of "7*10000 + 6*1000 + 9*100 + 
5*10 + 2" divided by 8 is equivalent to remainder 
of following : 
0 + 0 + 9*100 + 5*10 + 2 = 52
Therefore we can say that the whole number is 
divisible by 8 if 952 is divisible by 8.

Below is implementation of above fact :

C++

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// C++ program to find if a number is divisible by
// 8 or not
#include<bits/stdc++.h>
using namespace std;
  
// Function to find that number divisible by
// 8 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')%8 == 0);
  
    // If there is double digit
    if (n == 2)
        return (((str[n-2]-'0')*10 + (str[n-1]-'0'))%8 == 0);
  
    // If number formed by last three digits is
    // divisible by 8.
    int last = str[n-1] - '0';
    int second_last = str[n-2] - '0';
    int third_last = str[n-3] - '0';
  
    return ((third_last*100 + second_last*10 + last) % 8 == 0);
}
  
// Driver code
int main()
{
    string str = "76952";
    check(str)?  cout << "Yes" : cout << "No ";
    return 0;
}

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Java

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// Java program to find if a number is
// divisible by 8 or not
class IsDivisible
{
    // Function to find that number divisible by
    // 8 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')%8 == 0);
       
        // If there is double digit
        if (n == 2)
            return (((str.charAt(n-2)-'0')*10 + (str.charAt(n-1)-'0'))%8 == 0);
       
        // If number formed by last three digits is
        // divisible by 8.
        int last = str.charAt(n-1) - '0';
        int second_last = str.charAt(n-2) - '0';
        int third_last = str.charAt(n-3) - '0';
       
        return ((third_last*100 + second_last*10 + last) % 8 == 0);
    }
      
    // main function
    public static void main (String[] args) 
    {
        String str = "76952";
        if(check(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }

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Python3

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# Python 3 program to find 
# if a number is divisible
# by 8 or not
  
  
# Function to find that
# number divisible by 8
# or not
def check(st) :
    n = len(st)
      
    # Empty string
    if (n == 0) :
        return False
  
    # If there is single digit
    if (n == 1) :
        return ((int)(st[0]) % 8 == 0)
  
    # If there is double digit
    if (n == 2) :
        return ((int)(st[n - 2]) * 10 +
          ((int)(str[n - 1]) % 8 == 0))
  
    # If number formed by last
    # three digits is divisible
    # by 8.
    last = (int)(st[n - 1])
    second_last = (int)(st[n - 2])
    third_last = (int)(st[n - 3])
  
    return ((third_last*100 + second_last*10 +
                               last) % 8 == 0)
  
  
# Driver code
st = "76952"
  
if(check(st)) :
    print("Yes")
else
    print("No ")
      
# This code is contributed by Nikita tiwari

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C#

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// C# program to find if a number
// is divisible by 8 or not
using System;
  
class IsDivisible
{
    // Function to find that number 
    // divisible by 8 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') %8  == 0);
      
        // If there is double digit
        if (n == 2)
            return (((str[n - 2] - '0') * 10 + 
            (str[n - 1] - '0')) % 8 == 0);
      
        // If number formed by last three 
        // digits is divisible by 8
        int last = str[n - 1] - '0';
        int second_last = str[n - 2] - '0';
        int third_last = str[n - 3] - '0';
      
        return ((third_last * 100 + second_last  
                        * 10 + last) % 8 == 0);
    }
      
    // Driver Code
    public static void Main () 
    {
        String str = "76952";
        if(check(str))
            Console.Write("Yes");
        else
            Console.Write("No");
    }
  
// This Code is contributed by Nitin Mittal.

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PHP

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<?php
// PHP program to find if a number 
// is divisible by 8 or not
  
// Function to find that number
// divisible by 8 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') %
                          8 == 0);
  
    // If there is double digit
    if ($n == 2)
        return ((($str[$n - 2] - '0') * 
               10 + ($str[$n - 1] - '0')) 
                                % 8 == 0);
  
    // If number formed by last three 
    // digits is divisible by 8.
    $last = $str[$n - 1] - '0';
    $second_last = $str[$n - 2] - '0';
    $third_last = $str[$n - 3] - '0';
  
    return (($third_last * 100 + 
             $second_last * 10 + 
             $last) % 8 == 0);
}
  
// Driver code
$str = "76952";
$x = check($str)? "Yes" : "No ";
echo($x);
  
// This code is contributed by Ajit.
?>

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Output:

Yes

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Improved By : nitin mittal, jit_t



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