Count numbers in range L-R that are divisible by all of its non-zero digits

Given a range l – r (inclusive), count the numbers that are divisible by all of its non-zero digits.

Examples:

Input : 1 9 
Output : 9
Explanation: 
all the numbers are divisible by 
their digits in the range 1-9.

Input : 10 20 
Output : 5
Explanation: 
10, 11, 12, 15, 20

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

Approach:
1. Run a loop to generate every number from l and r.
2. Check if every non-zero digit of that number divides the number or not.
3. Keep a count of all numbers that are completely divisible by its digits.
4. Print the count of numbers.

Below is the implementation of the above approach:

C++

// C++ program to 
// Count numbers in 
// range L-R that are 
// divisible by 
// all of its non-zero 
// digits 
#include <bits/stdc++.h> 
using namespace std; 
  
// check if the number is  
// divisible by the digits. 
bool check(int n) 
{ 
    int m = n; 
    while (n) { 
        int r = n % 10; 
        if (r > 0)  
            if ((m % r) != 0) 
                return false;         
        n /= 10; 
    } 
  
    return true; 
} 
  
// function to calculate the 
// number of numbers 
int count(int l, int r) 
{ 
    int ans = 0; 
    for (int i = l; i <= r; i++)  
        if (check(i)) 
            ans += 1;     
    return ans; 
} 
  
// Driver function 
int main() 
{ 
    int l = 10, r = 20; 
    cout << count(l, r); 
    return 0; 
} 

Java

// Java program to Count  
// numbers in range L-R 
// that are divisible by 
// all of its non-zero  
// digits 
import java.io.*; 
  
class GFG { 
  
    // check if the number 
    // is divisible by the 
    // digits. 
    static boolean check(int n) 
    { 
        int m = n; 
      
        while (n != 0) 
        { 
            int r = n % 10; 
          
            if (r > 0)  
                if ((m % r) != 0) 
                    return false;      
          
            n /= 10; 
        } 
      
        return true; 
    } 
      
    // function to calculate 
    // the number of numbers 
    static int count(int l, int r) 
    { 
        int ans = 0; 
          
        for (int i = l; i <= r; i++)  
            if (check(i)) 
                ans += 1;  
        return ans; 
    } 
      
    // Driver function 
    public static void main(String args[]) 
    { 
        int l = 10, r = 20; 
          
        System.out.println(count(10, 20)); 
    } 
} 
  
// This code is contributed by Nikita Tiwari. 

Python3

# Python 3 program 
# to Count numbers in 
# range L-R that are  
# divisible by all of 
# its non-zero digits 
  
  
# check if the number is  
# divisible by the digits. 
def check(n) : 
    m = n 
    while (n != 0) : 
        r = n % 10
        if (r > 0) : 
            if ((m % r) != 0) : 
                return False    
        n = n // 10
      
    return True
      
  
# function to calculate the 
# number of numbers 
def count(l, r) : 
    ans = 0
    for i in range(l, r+1) : 
        if (check(i)) : 
            ans = ans + 1
    return ans 
  
# Driver function 
l = 10
r = 20
print(count(l, r)) 
  
# This code is contributed by Nikita Tiwari. 

C#

// Java program to Count  
// numbers in range L-R 
// that are divisible by 
// all of its non-zero  
// digits 
using System; 
  
class GFG { 
  
    // check if the number 
    // is divisible by the 
    // digits. 
    static bool check(int n) 
    { 
        int m = n; 
      
        while (n != 0) 
        { 
            int r = n % 10; 
          
            if (r > 0)  
                if ((m % r) != 0) 
                    return false;  
          
            n /= 10; 
        } 
      
        return true; 
    } 
      
    // function to calculate 
    // the number of numbers 
    static int count(int l, int r) 
    { 
        int ans = 0; 
          
        for (int i = l; i <= r; i++)  
            if (check(i)) 
                ans += 1;  
        return ans; 
    } 
      
    // Driver function 
    public static void Main() 
    { 
        int l = 10, r = 20; 
          
        Console.WriteLine(count(l, r)); 
    } 
} 
  
// This code is contributed by Vt_m. 

PHP

<?php 
// PHP program to Count numbers 
// in range L-R that are 
// divisible by all of its  
// non-zero digits 
  
// check if the number is  
// divisible by the digits. 
function check($n) 
{ 
    $m = $n; 
    while ($n) { 
        $r = $n % 10; 
        if ($r > 0)  
            if (($m % $r) != 0) 
                return false;      
        $n /= 10; 
    } 
  
    return true; 
} 
  
// function to calculate the 
// number of numbers 
function countIn($l, $r) 
{ 
    $ans = 0; 
    for ($i = $l; $i <= $r; $i++)  
        if (check($i)) 
            $ans += 1;  
              
    return $ans; 
  
} 
  
// Driver function 
$l = 10; $r = 20; 
echo countIn($l, $r); 
  
// This code is contributed ajit 
?> 

Output:

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Suggest a Topic

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

C++

Java

Python3

C#

PHP

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