# Check whether a large number is divisible by 53 or not

Given a large number in the form of a string N, the task is to check whether the number is divisible by 53 or not.

Examples:

Input: N = 5299947
Output: Yes

Input: N = 54
Output: No

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Extract the last digit of the given string N and remove it.
• Multiply that digit by 37.
• Subtract the product calculated in the above step from the remaining number.
• Continue until we reduce the given string to a 3 or four digit number.
• Convert the remaining string to its corresponding integer form and check if it is divisible by 53 or not.

Below is the implementation of the above approach:

## C++

 `// C++ program to check ` `// whether a number ` `// is divisible by 53 or not ` `#include ` `using` `namespace` `std; ` ` `  `// Function to check if the ` `// number is divisible by 53 or not ` `bool` `isDivisible(string s) ` `{ ` `    ``int` `flag = 0; ` `    ``while` `(s.size() > 4) { ` ` `  `        ``int` `l = s.size() - 1; ` `        ``int` `x = (s[l] - ``'0'``) * 37; ` ` `  `        ``reverse(s.begin(), s.end()); ` `        ``s.erase(0, 1); ` ` `  `        ``int` `i = 0, carry = 0; ` `        ``while` `(x) { ` `            ``int` `d = (s[i] - ``'0'``) ` `                    ``- (x % 10) ` `                    ``- carry; ` `            ``if` `(d < 0) { ` `                ``d += 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``s[i] = (``char``)(d + ``'0'``); ` `            ``x /= 10; ` `            ``i++; ` `        ``} ` ` `  `        ``while` `(carry && i < l) { ` `            ``int` `d = (s[i] - ``'0'``) - carry; ` `            ``if` `(d < 0) { ` `                ``d += 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``s[i] = (``char``)(d + ``'0'``); ` ` `  `            ``i++; ` `        ``} ` ` `  `        ``reverse(s.begin(), s.end()); ` `    ``} ` ` `  `    ``int` `num = 0; ` `    ``for` `(``int` `i = 0; i < s.size(); i++) { ` `        ``num = num * 10 + (s[i] - ``'0'``); ` `    ``} ` ` `  `    ``if` `(num % 53 == 0) ` `        ``return` `true``; ` `    ``else` `        ``return` `false``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``string N = ``"18432462191076"``; ` ` `  `    ``if` `(isDivisible(N)) ` `        ``cout << ``"Yes"` `<< endl; ` `    ``else` `        ``cout << ``"No"` `<< endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to check whether  ` `// a number is divisible by 53 or not ` `import` `java.util.*; ` ` `  `class` `GFG{ ` ` `  `// Function to check if the ` `// number is divisible by 53 or not ` `static` `boolean` `isDivisible(``char` `[]s) ` `{ ` `    ``while` `(s.length > ``4``) ` `    ``{ ` `        ``int` `l = s.length - ``1``; ` `        ``int` `x = (s[l] - ``'0'``) * ``37``; ` ` `  `        ``s = reverse(s); ` `        ``s = Arrays.copyOfRange(s, ``1``, s.length); ` ` `  `        ``int` `i = ``0``, carry = ``0``; ` `        ``while` `(x > ``0``)  ` `        ``{ ` `            ``int` `d = (s[i] - ``'0'``) -  ` `                        ``(x % ``10``) -  ` `                        ``carry; ` `                     `  `            ``if` `(d < ``0``) ` `            ``{ ` `                ``d += ``10``; ` `                ``carry = ``1``; ` `            ``} ` `            ``else` `                ``carry = ``0``; ` ` `  `            ``s[i] = (``char``)(d + ``'0'``); ` `            ``x /= ``10``; ` `            ``i++; ` `        ``} ` ` `  `        ``while` `(carry > ``0` `&& i < l) ` `        ``{ ` `            ``int` `d = (s[i] - ``'0'``) - carry; ` `            ``if` `(d < ``0``) ` `            ``{ ` `                ``d += ``10``; ` `                ``carry = ``1``; ` `            ``} ` `            ``else` `                ``carry = ``0``; ` ` `  `            ``s[i] = (``char``)(d + ``'0'``); ` `            ``i++; ` `        ``} ` `        ``s = reverse(s); ` `    ``} ` ` `  `    ``int` `num = ``0``; ` `    ``for``(``int` `i = ``0``; i < s.length; i++)  ` `    ``{ ` `       ``num = num * ``10` `+ (s[i] - ``'0'``); ` `    ``} ` ` `  `    ``if` `(num % ``53` `== ``0``) ` `        ``return` `true``; ` `    ``else` `        ``return` `false``; ` `} ` ` `  `static` `char``[] reverse(``char` `[]a) ` `{ ` `    ``int` `l, r = a.length - ``1``; ` `     `  `    ``for``(l = ``0``; l < r; l++, r--) ` `    ``{ ` `       ``char` `temp = a[l]; ` `            ``a[l] = a[r]; ` `            ``a[r] = temp; ` `    ``} ` `    ``return` `a; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``String N = ``"18432462191076"``; ` ` `  `    ``if` `(isDivisible(N.toCharArray())) ` `        ``System.out.print(``"Yes"` `+ ``"\n"``); ` `    ``else` `        ``System.out.print(``"No"` `+ ``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by Rohit_ranjan `

## Python3

 `# Python3 program to check whether a   ` `# number is divisible by 53 or not ` ` `  `# Function to check if the ` `# number is divisible by 53 or not ` `def` `isDivisible(s): ` `     `  `    ``flag ``=` `0` `     `  `    ``while` `(``len``(s) > ``4``): ` `        ``l ``=` `len``(s) ``-` `1` `        ``x ``=` `(``ord``(s[l]) ``-` `ord``(``'0'``)) ``*` `37` ` `  `        ``s ``=` `s[::``-``1``] ` `        ``s ``=` `s.replace(``'0'``, '', ``1``) ` ` `  `        ``i ``=` `0` `        ``carry ``=` `0` `         `  `        ``while` `(x): ` `            ``d ``=` `((``ord``(s[i]) ``-` `ord``(``'0'``)) ``-`  `                 ``(x ``%` `10``) ``-` `carry) ` `            ``if` `(d < ``0``): ` `                ``d ``+``=` `10` `                ``carry ``=` `1` `            ``else``: ` `                ``carry ``=` `0` `                 `  `            ``s ``=` `s.replace(s[i], ``chr``(d ``+` `ord``(``'0'``)), ``1``) ` `            ``x ``/``/``=` `10` `            ``i ``+``=` `1` ` `  `        ``while` `(carry ``and` `i < l): ` `            ``d ``=` `(``ord``(s[i]) ``-` `ord``(``'0'``)) ``-` `carry ` `             `  `            ``if` `(d < ``0``): ` `                ``d ``+``=` `10` `                ``carry ``=` `1` `            ``else``: ` `                ``carry ``=` `0` `             `  `            ``s ``=` `s.replace(s[i], ``chr``(d ``+` `ord``(``'0'``)), ``1``) ` `            ``i ``+``=` `1` `        ``s ``=` `s[::``-``1``] ` ` `  `    ``num ``=` `0` `    ``for` `i ``in` `range``(``len``(s)): ` `        ``num ``=` `num ``*` `10` `+` `(``ord``(s[i]) ``-` `ord``(``'0'``)) ` ` `  `    ``if` `(num ``%` `53` `=``=` `0``): ` `        ``return` `True` `    ``else``: ` `        ``return` `False` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `     `  `    ``N ``=` `"1843246219106"` ` `  `    ``if` `(isDivisible(N)): ` `        ``print``(``"No"``) ` `    ``else``: ` `        ``print``(``"Yes"``) ` ` `  `# This code is contributed by Surendra_Gangwar `

## C#

 `// C# program to check whether   ` `// a number is divisible by 53 or not  ` `using` `System;  ` `using` `System.Collections;  ` `using` `System.Collections.Generic;  ` ` `  `class` `GFG{ ` `     `  `// Function to check if the ` `// number is divisible by 53 or not ` `static` `bool` `isDivisible(``char` `[]s) ` `{ ` `    ``while` `(s.Length > 4) ` `    ``{ ` `        ``int` `l = s.Length - 1; ` `        ``int` `x = (s[l] - ``'0'``) * 37; ` ` `  `        ``s = reverse(s); ` `         `  `        ``char` `[]tmp = ``new` `char``[s.Length - 1]; ` `         `  `        ``Array.Copy(s, 1, tmp, 0, s.Length - 1); ` `        ``s = tmp; ` `         `  `        ``int` `i = 0, carry = 0; ` `        ``while` `(x > 0)  ` `        ``{ ` `            ``int` `d = (s[i] - ``'0'``) -  ` `                       ``(x % 10) - carry; ` `                        `  `            ``if` `(d < 0) ` `            ``{ ` `                ``d += 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``s[i] = (``char``)(d + ``'0'``); ` `            ``x /= 10; ` `            ``i++; ` `        ``} ` ` `  `        ``while` `(carry > 0 && i < l) ` `        ``{ ` `            ``int` `d = (s[i] - ``'0'``) - carry; ` `            ``if` `(d < 0) ` `            ``{ ` `                ``d += 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``s[i] = (``char``)(d + ``'0'``); ` `            ``i++; ` `        ``} ` `        ``s = reverse(s); ` `    ``} ` ` `  `    ``int` `num = 0; ` `    ``for``(``int` `i = 0; i < s.Length; i++)  ` `    ``{ ` `        ``num = num * 10 + (s[i] - ``'0'``); ` `    ``} ` ` `  `    ``if` `(num % 53 == 0) ` `        ``return` `true``; ` `    ``else` `        ``return` `false``; ` `} ` ` `  `static` `char``[] reverse(``char` `[]a) ` `{ ` `    ``int` `l, r = a.Length - 1; ` `     `  `    ``for``(l = 0; l < r; l++, r--) ` `    ``{ ` `        ``char` `temp = a[l]; ` `             ``a[l] = a[r]; ` `             ``a[r] = temp; ` `    ``} ` `    ``return` `a; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(``string``[] args) ` `{ ` `    ``string` `N = ``"18432462191076"``; ` ` `  `    ``if` `(isDivisible(N.ToCharArray())) ` `        ``Console.Write(``"Yes"` `+ ``"\n"``); ` `    ``else` `        ``Console.Write(``"No"` `+ ``"\n"``); ` `} ` `} ` ` `  `// This code is contributed by rutvik_56 `

Output:

```Yes
```

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