Check if a large number is divisible by 25 or not

Given a number, the task is to check if number is divisible by 25. The input number may be large and it may not be possible to store even if we use long long int.

Examples: 

Input  : n = 56945250
Output : Yes

Input  : n = 1234567589333100
Output : Yes

Input  : n = 3635883959606670431112222
Output : No

Since input number may be very large, we cannot use n % 25 to check if a number is divisible by 25 or not, especially in languages like C/C++. The idea is based on following fact.

A number is divisible by 25 if its digits 
last two digits will be 0  or divisible by 25 .

Illustration: 

For example, let us consider 769575 
Number formed by last two digits is = 75
Since 75 is divisible by 25 , answer is YES.

Let us consider 5325, we can write it as
5325 = 5*1000 + 3*100 + 2*10 + 5

The proof is based on below observation:
Remainder of 10i divided by 25 is 0 if i greater 
than or equal to two. Note than 100, 1000,
... etc lead to remainder 0 when divided by 25.

So remainder of " 5*1000 + 3*100 + 2*10 + 5" 
divided by 25 is equivalent to remainder 
of following : 
0 + 0 + 20 + 5 = 25

Since 25 is divisible by 25, answer is yes.

C++

// C++ program to find if a number is
// divisible by 25 or not
#include<bits/stdc++.h>
using namespace std;

// Function to find that number divisible
// by 25 or not.
bool isDivisibleBy25(string str)
{
    // If length of string is single digit then
    // it's not divisible by 25
    int n = str.length();
    if (n == 1)
        return false;

    return ( (str[n-1]-'0' == 0  &&
              str[n-2]-'0' == 0) ||
   ((str[n-2]-'0')*10 + (str[n-1]-'0'))%25 == 0 );
}

// Driver code
int main()
{
    string str = "76955";
    isDivisibleBy25(str)?  cout << "Yes" :
                           cout << "No ";
    return 0;
}

Java

// Java program to find if a number is
// divisible by 25 or not
class IsDivisible
{
    // Function to find that number divisible
    // by 25 or not.
    static boolean isDivisibleBy25(String str)
    {
        // If length of string is single digit then
        // it's not divisible by 25
        int n = str.length();
        if (n == 1)
            return false;

        return ( (str.charAt(n-1)-'0' == 0  &&
                  str.charAt(n-2)-'0' == 0) ||
        ((str.charAt(n-2)-'0')*10 + (str.charAt(n-1)-'0'))%25 == 0 );
    }

    // main function
    public static void main (String[] args)
    {
        String str = "76955";
        if(isDivisibleBy25(str))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}

Python3

# Python 3 program to find if
# a number is divisible by 25
# or not

# Function to find that
# number divisible by 25 or not.
def isDivisibleBy25(st) :

    # If length of string is
    # single digit then it's
    # not divisible by 25
    n = len(st)
    if (n == 1) :
        return False

    return ((int)(st[n-1]) == 0 and ((int)(st[n-2])== 0) or
           ((int)(st[n-2])*10 + (int)(st[n-1])%25 == 0))

# Driver code
st = "76955"
if(isDivisibleBy25(st)) :
    print("Yes")
else :
    print("No")


# This code is contributed by Nikita Tiwari.

C#

// C# program to find if a number
// is divisible by 25 or not
using System;

class IsDivisible
{
    // Function to find that number
    // divisible by 25 or not.
    static bool isDivisibleBy25(String str)
    {
        // If length of string is single digit then
        // then it's not divisible by 25
        int n = str.Length;
        if (n == 1)
            return false;

        return ((str[n - 1] - '0' == 0 &&
                 str[n - 2] - '0' == 0) ||
                ((str[n - 2] - '0') * 10 +
                 (str[n - 1] - '0')) % 25 == 0);
    }

    // Driver Code
    public static void Main ()
    {
        String str = "76955";
        if(isDivisibleBy25(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 25 or not

// Function to find that number
//  divisible by 25 or not.
function isDivisibleBy25($str)
{

    // If length of string
    // is single digit then
    // it's not divisible by 25
    $n = strlen($str);
    if ($n == 1)
        return false;

    return ( ($str[$n - 1] -'0' == 0 &&
              $str[$n - 2] -'0' == 0) ||
            (($str[$n - 2] -'0') * 10 +
             ($str[$n - 1] - '0')) % 25 == 0 );
}

// Driver code
$str = "76955";
$x = isDivisibleBy25($str) ? "Yes" : "No ";
echo($x);

// This code is contributed by Ajit.
?>

Javascript

<script>

// Javascript program to find if a number
// is divisible by 25 or not

// Function to find that number
// divisible by 25 or not
function isDivisibleBy25(str)
{

    // If length of string
    // is single digit then
    // it's not divisible by 25
    n = str.length;

    if (n == 1)
        return false;

    return ((str[n - 1] -'0' == 0 &&
             str[n - 2] -'0' == 0) ||
           ((str[n - 2] -'0') * 10 +
            (str[n - 1] - '0')) % 25 == 0);
}

// Driver Code
var str = "76955";
var x = isDivisibleBy25(str) ? "Yes" : "No";

document.write (x);

// This code is contributed by bunnyram19

</script>

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.
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