# Check if Decimal representation of an Octal number is divisible by 7

Given an Octal number N. The task is to write a program to check if the Decimal representation of the given octal number N is divisible by 7 or not.

Examples:

```Input: N = 112
Output: NO
Equivalent Decimal = 74
7410 = 7 * 10 1 + 4 * 100
1128 = 1 * 82 + 1 * 81 + 2 * 80

Input: N = 25
Output: YES
Decimal Equivalent = 21
```

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

The idea is to note that, 8 % 7 will return 1. Thus, when we expand octal representation and take its modulo 7 all powers of 8 in individual terms will reduce to 1. So, if the sum of all the digits in octal representation is divisible by 7 then, the corresponding decimal number will be divisible by 7.

Below is the implementation of the above approach:

## C++

 `// CPP program to check if Decimal representation ` `// of an Octal number is divisible by 7 or not ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to check Divisibility ` `int` `check(``int` `n) ` `{ ` `    ``int` `sum = 0; ` ` `  `    ``// Sum of all individual digits ` `    ``while` `(n != 0) { ` `        ``sum += n % 10; ` `        ``n = n / 10; ` `    ``} ` ` `  `    ``// Condition ` `    ``if` `(sum % 7 == 0) ` `        ``return` `1; ` `    ``else` `        ``return` `0; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``// Octal number ` `    ``int` `n = 25; ` ` `  `    ``(check(n) == 1) ? cout << ``"YES"` `                    ``: cout << ``"NO"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to check if Decimal  ` `// representation of an Octal number  ` `// is divisible by 7 or not ` `import` `java.util.*; ` `import` `java.lang.*; ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to check Divisibility ` `static` `int` `check(``int` `n) ` `{ ` `    ``int` `sum = ``0``; ` ` `  `    ``// Sum of all individual digits ` `    ``while` `(n != ``0``)  ` `    ``{ ` `        ``sum += n % ``10``; ` `        ``n = n / ``10``; ` `    ``} ` ` `  `    ``// Condition ` `    ``if` `(sum % ``7` `== ``0``) ` `        ``return` `1``; ` `    ``else` `        ``return` `0``; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String args[]) ` `{ ` `    ``// Octal number ` `    ``int` `n = ``25``; ` ` `  `    ``String s=(check(n) == ``1``) ?  ` `                       ``"YES"` `: ``"NO"``; ` `    ``System.out.println(s); ` `} ` `} ` ` `  `// This code is contributed ` `// by Subhadeep `

## Python 3

 `# Python 3 program to check if  ` `# Decimal representation of an ` `# Octal number is divisible by  ` `# 7 or not ` ` `  `# Function to check Divisibility ` `def` `check(n): ` ` `  `    ``sum` `=` `0` ` `  `    ``# Sum of all individual digits ` `    ``while` `n !``=` `0` `: ` `        ``sum` `+``=` `n ``%` `10` `        ``n ``=` `n ``/``/` `10` ` `  `    ``# Condition ` `    ``if` `sum` `%` `7` `=``=` `0` `: ` `        ``return` `1` `    ``else``: ` `        ``return` `0` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``# Octal number ` `    ``n ``=` `25` ` `  `    ``print``((``"YES"``) ``if` `check(n) ``=``=` `1`  `                  ``else` `print``(``"NO"``)) ` ` `  `# This code is contributed ` `# by ChitraNayal `

## C#

 `// C# program to check if Decimal ` `// representation of an Octal  ` `// number is divisible by 7 or not ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `    ``// Function to check Divisibility ` `    ``static` `int` `check(``int` `n) ` `    ``{ ` `            ``int` `sum = 0; ` `     `  `        ``// Sum of all individual digits ` `        ``while` `(n != 0) ` `        ``{ ` `            ``sum += n % 10; ` `            ``n = n / 10; ` `        ``} ` `     `  `    ``// Condition ` `    ``if` `(sum % 7 == 0) ` `        ``return` `1; ` `    ``else` `        ``return` `0; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``// Octal number ` `    ``int` `n = 25; ` `     `  `    ``String s=(check(n) == 1) ?  ` `                       ``"YES"` `: ``"NO"``; ` `    ``Console.WriteLine(s); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Kirti_Mangal `

## PHP

 ` `

Output:

```YES
```

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