Skip to content
Related Articles

Related Articles

Check if a large number is divisible by 8 or not
  • Difficulty Level : Easy
  • Last Updated : 23 Mar, 2021

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++




// 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;
}

Java




// 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");
    }
}

Python3




# 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

C#




// 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.

PHP




<?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.
?>

Javascript




<script>
 
// JavaScript program for the above approach
 
    // Function to find that number 
    // divisible by 8 or not
    function check(str)
    {
        let 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
        let last = str[n - 1] - '0';
        let second_last = str[n - 2] - '0';
        let third_last = str[n - 3] - '0';
       
        return ((third_last * 100 + second_last  
                        * 10 + last) % 8 == 0);
    }
 
// Driver Code
     
     let str = "76952";
     if(check(str))
        document.write("Yes");
     else
         document.write("No");
 
// This code is contributed by splevel62.
</script>

Output:

Yes

This article is contributed by DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@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.
 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up
Recommended Articles
Page :