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++
// 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 Divisibilityint 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 Codeint 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 notimport java.util.*;import java.lang.*;import java.io.*;class GFG{ // Function to check Divisibilitystatic 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 Codepublic 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 Divisibilitydef 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 Codeif __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 notusing 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 Codepublic 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
<?php// PHP program to check if // Decimal representation of// an Octal number is divisible // by 7 or not// Function to check Divisibilityfunction 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?> |
Javascript
<script>// Javascript program to check if Decimal representation// of an Octal number is divisible by 7 or not// Function to check Divisibilityfunction check(n){ let sum = 0; // Sum of all individual digits while (n != 0) { sum += n % 10; n = Math.floor(n / 10); } // Condition if (sum % 7 == 0) return 1; else return 0;}// Driver Code // Octal number let n = 25; (check(n) == 1) ? document.write("YES") : document.write("NO");// This code is contributed by Mayank Tyagi</script> |
Output:
YES
Time Complexity: O(log10n)
Auxiliary Space: O(1)
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