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Find a N-digit number such that it is not divisible by any of its digits

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  • Last Updated : 06 Sep, 2022
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Given an integer N, the task is to find any N-digit positive number (except for zeros) such that it is not divisible by any of its digits. If it is not possible to find any such number then print -1.
Note: There can be more than one such number for the same N-digit.
 

Examples:  

Input: N = 2  
Output: 23
23 is not divisible by 2 or 3

Input: N = 3
Output: 239

 

Approach: 
The easiest solution to this problem can be thought of with the help of digits ‘4’ and ‘5’. 
 

  1. Since, in order for a number to be divisible by 5, the number must end with 0 or 5; and in order for it to be divisible by 4, the last two digits if the number must be divisible by 4.
  2. Therefore, a shortcut method can be applied to prevent both of the divisibility criteria of 4 and as well as of 5, as: 
  • To prevent a number from being divisible by 5, the number can contain 5 for every other digit except for last digit. 
     
Therefore for N digit number,
(N - 1) digits must be 5 = 5555...(N-1 times)d
where d is the Nth digit
  • To prevent a number from being divisible by 4, the number can contain 5 at the second last digit and 4 at the last digit. 
     
Therefore for N digit number,
Last digit must be 4 = 5555...(N-1 times)4

Below is the implementation of the above approach: 
 

CPP




// CPP program to find N digit number such
// that it is not divisible by any of its digits
 
#include <bits/stdc++.h>
using namespace std;
 
// Function that print the answer
void findTheNumber(int n)
{
    // if n == 1 then it is
    // not possible
    if (n == 1) {
        cout << "Impossible" << endl;
        return;
    }
 
    // loop to n-1 times
    for (int i = 0; i < n - 1; i++) {
        cout << "5";
    }
 
    // print 4 as last digit of
    // the number
    cout << "4";
}
 
// Driver code
int main()
{
    int n = 12;
 
    // Function call
    findTheNumber(n);
 
    return 0;
}

Java




// JAVA program to find N digit number such
// that it is not divisible by any of its digits
class GFG{
  
// Function that print the answer
static void findTheNumber(int n)
{
    // if n == 1 then it is
    // not possible
    if (n == 1) {
        System.out.print("Impossible" +"\n");
        return;
    }
  
    // loop to n-1 times
    for (int i = 0; i < n - 1; i++) {
        System.out.print("5");
    }
  
    // print 4 as last digit of
    // the number
    System.out.print("4");
}
  
// Driver code
public static void main(String[] args)
{
    int n = 12;
  
    // Function call
    findTheNumber(n);
  
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python3 program to find N digit number such
# that it is not divisible by any of its digits
  
# Function that print answer
def findTheNumber(n):
    # if n == 1 then it is
    # not possible
    if (n == 1):
        print("Impossible")
        return
  
    # loop to n-1 times
    for i in range(n-1):
        print("5",end="")
  
    # print as last digit of
    # the number
    print("4")
  
# Driver code
if __name__ == '__main__':
    n = 12
  
    #Function call
    findTheNumber(n)
 
# This code is contributed by mohit kumar 29

C#




// C# program to find N digit number such
// that it is not divisible by any of its digits
using System;
 
class GFG{
 
// Function that print the answer
static void findTheNumber(int n)
{
    // if n == 1 then it is
    // not possible
    if (n == 1) {
        Console.Write("Impossible" +"\n");
        return;
    }
 
    // loop to n-1 times
    for (int i = 0; i < n - 1; i++) {
        Console.Write("5");
    }
 
    // print 4 as last digit of
    // the number
    Console.Write("4");
}
 
// Driver code
public static void Main(String[] args)
{
    int n = 12;
 
    // Function call
    findTheNumber(n);
}
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
 
// Javascript program to find N digit number such
// that it is not divisible by any of its digits
 
// Function that print the answer
function findTheNumber(n)
{
    // if n == 1 then it is
    // not possible
    if (n == 1) {
        document.write( "Impossible" );
        return;
    }
 
    // loop to n-1 times
    for (var i = 0; i < n - 1; i++) {
        document.write( "5");
    }
 
    // print 4 as last digit of
    // the number
    document.write( "4");
}
 
// Driver code
var n = 12;
// Function call
findTheNumber(n);
 
// This code is contributed by rutvik_56.
</script>

Output: 

555555555554

 

Time complexity: O(N), where N is the required size of the number.
 Auxiliary Space: O(1), as constant space is required.


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