Check if a number is divisible by 47 or not

Given a number N, the task is to check whether the number is divisible by 47 or not.

Examples:

Input: N = 1645
Output: yes
Explanation:
47 * 35 = 1645

Input: N = 4606
Output: yes
Explanation:
47 * 98 = 4606

Approach: The divisibility test of 47 is:



  1. Extract the last digit.
  2. Subtract 14 * last digit from the remaining number obtained after removing the last digit.
  3. Repeat the above steps until a two-digit number, or zero, is obtained.
  4. If the two-digit number is divisible by 47, or it is 0, then the original number is also divisible by 47.

For example:

If N = 59173

Step 1:
  N = 59173
  Last digit = 3
  Remaining number = 5917
  Subtracting 14 times last digit
  Resultant number = 5917 - 14*3 = 5875

Step 2:
  N = 5875
  Last digit = 5
  Remaining number = 587
  Subtracting 14 times last digit
  Resultant number = 587 - 14*5 = 517

Step 3:
  N = 517
  Last digit = 7
  Remaining number = 51
  Subtracting 14 times last digit
  Resultant number = 51 - 14*7 = -47

Step 4:
  N = -47
  Since N is a two-digit number,
  and -47 is divisible by 47

Therefore N = 59173 is also divisible by 47

Below is the implementation of the above approach:

C++

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// C++ program to check whether a number
// is divisible by 47 or not
#include<bits/stdc++.h>
#include<stdlib.h>
  
using namespace std;
  
// Function to check if the number is  divisible by 47 or not 
bool isDivisible(int n)  
{
    int d;
    // While there are at least two digits 
    while (n / 100) 
    {
   
        // Extracting the last 
        d = n % 10;
   
        // Truncating the number 
        n /= 10;
   
        // Subtracting fourteen times the last 
        // digit to the remaining number 
        n = abs(n-(d * 14));
    }
    // Finally return if the two-digit
    // number is divisible by 47 or not
    return (n % 47 == 0) ;
}
  
// Driver Code 
int main() {
    int N = 59173;
   
    if (isDivisible(N)) 
        cout<<"Yes"<<endl ;
    else 
        cout<<"No"<<endl ;
     
     return 0;     
}    
  
// This code is contributed by ANKITKUMAR34

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Java

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// Java program to check whether a number
// is divisible by 47 or not
import java.util.*;
  
class GFG{
   
// Function to check if the number is  divisible by 47 or not 
static boolean isDivisible(int n)  
{
    int d;
      
    // While there are at least two digits 
    while ((n / 100) > 0
    {
    
        // Extracting the last 
        d = n % 10;
    
        // Truncating the number 
        n /= 10;
    
        // Subtracting fourteen times the last 
        // digit to the remaining number 
        n = Math.abs(n - (d * 14));
    }
  
    // Finally return if the two-digit
    // number is divisible by 47 or not
    return (n % 47 == 0) ;
}
   
// Driver Code 
public static void main(String[] args) {
    int N = 59173;
    
    if (isDivisible(N)) 
        System.out.print("Yes") ;
    else
        System.out.print("No");
      
 }     
}    
  
// This code is contributed by PrinciRaj1992

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Python 3

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# Python program to check if a number
# is divisible by 47 or not
  
# Function to check if the number is 
# divisible by 47 or not 
def isDivisible(n) : 
   
    # While there are at least two digits 
    while n // 100
   
        # Extracting the last 
        d = n % 10
   
        # Truncating the number 
        n //= 10
   
        # Subtracting fourteen times the last 
        # digit to the remaining number 
        n = abs(n- (d * 14))
   
    # Finally return if the two-digit
    # number is divisible by 43 or not
    return (n % 47 == 0
   
# Driver Code 
if __name__ == "__main__"
       
    n = 59173
  
    if (isDivisible(n)) : 
        print("Yes"
    else
        print("No"

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C#

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// C# program to check whether a number
// is divisible by 47 or not
using System; 
          
class GFG 
      
// Function to check if the number is divisible by 47 or not 
static bool isDivisible(int n) 
{
    int d;
      
    // While there are at least two digits 
    while (n / 100 > 0) 
    {
      
        // Extracting the last 
        d = n % 10;
      
        // Truncating the number 
        n /= 10;
      
        // Subtracting fourteen times the last 
        // digit to the remaining number 
        n = Math.Abs(n - (d * 14));
    }
      
    // Finally return if the two-digit
    // number is divisible by 47 or not
    return (n % 47 == 0);
}
      
// Driver Code 
public static void Main() 
    int N = 59173;
      
    if (isDivisible(N)) 
        Console.WriteLine("Yes");
    else
        Console.WriteLine("No");
  
// This code is contributed by mohit kumar 29. 

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Output:

Yes

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