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

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++

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// CPP program to check if Decimal representation
// of an Octal number is divisible by 7 or not
  
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python 3

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# 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

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C#

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// 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

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PHP

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<?php
// PHP program to check if 
// Decimal representation of
// an Octal number is divisible 
// by 7 or not
  
// Function to check Divisibility
function check($n)
{
    $sum = 0;
  
    // Sum of all individual digits
    while ($n != 0) 
    {
        $sum += $n % 10;
        $n = (int)($n / 10);
    }
  
    // Condition
    if ($sum % 7 == 0)
        return 1;
    else
        return 0;
}
  
// Driver Code
  
// Octal number
$n = 25;
  
(check($n) == 1) ? 
  print("YES\n") : 
   print("NO\n");
      
// This Code is contributed 
// by mits
?>

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Output:

YES


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