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Smallest N digit number with none of its digits as its divisor
  • Last Updated : 19 Oct, 2020

Given an integer N. The task is to find the smallest N digit number S, such that S is not divisible by any of its digits. Print -1 if no such number is possible.
Examples: 

Input: N = 2 
Output: 23 
Explanation: 23 is the smallest two-digit number that is not divisible by any of its digits.
Input: N = 1 
Output: -1 
Explanation: Every single digit number is divisible by itself.
Input: N = 4 
Output: 2227 
Explanation: 2227 is the smallest four-digit number that is not divisible by any of its digits. 
 

Approach: 

  • The approach is to find the smallest and largest possible N-digit number say these numbers are L and R respectively.
  • Iterate over the range [L, R].
  • For each number in the range, extract every digit of that number and check if the number is divisible by that digit.
  • If at least one digit of the number divides it, discard that number and iterate to check the next number.
  • If none of the digits of that number divides it, then print that number and break out of the loop. This number so found is the smallest number.

Below is the implementation of the above approach: 
 

C++

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// C++ Program for the given problem
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate power
int power(int a, int b)
{
    if (b == 0)
        return 1;
    if (b == 1)
        return a;
 
    int tmp = power(a, b / 2);
 
    int result = tmp * tmp;
 
    if (b % 2 == 1)
        result *= a;
 
    return result;
}
 
// Function to check if the
// N-digit number satifies the
// given condition or not
bool check(int n)
{
    int temp = n;
    while (temp > 0) {
 
        // Getting the last digit
        int last_digit = temp % 10;
 
        // Every number is divisible
        // by 1 and dividing a number
        // by 0 isn't possible. Thus
        // numbers with 0 as a digit
        // must be discarded.
        if (last_digit == 0
            || last_digit == 1)
            return false;
 
        // If any digit divides the
        // number, return false
        if (n % last_digit == 0)
            return false;
        temp = temp / 10;
    }
 
    // If no digit divides the
    // number, return true;
    return true;
}
 
// Function to find the smallest
// number not divisible by any
// of its digits.
void solve(int n)
{
    // Get the lower range of n
    // digit number
    int L = power(10, n - 1);
 
    // Get the high range of n
    // digit number
    int R = power(10, n) - 1;
 
    int flag = 0;
 
    // check all the N-digit numbers
    for (int i = L; i <= R; i++) {
 
        bool answer = check(i);
 
        // If the first number to satify
        // the constraints is found
        // print it, set the flag value
        // and break out of the loop.
        if (answer == true) {
 
            cout << i << endl;
            flag++;
            break;
        }
    }
 
    // If no such digit found,
    // return -1 as per problem statement
    if (flag == 0)
        cout << -1 << endl;
}
 
// Driver Code
int main()
{
    int N = 4;
    solve(N);
}

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Java

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// Java program for the given problem
import java.util.*;
 
class GFG{
     
// Function to calculate power
static int power(int a, int b)
{
    if (b == 0)
        return 1;
    if (b == 1)
        return a;
         
    int tmp = power(a, b / 2);
    int result = tmp * tmp;
     
    if (b % 2 == 1)
        result *= a;
 
    return result;
}
 
// Function to check if the
// N-digit number satifies the
// given condition or not
static boolean check(int n)
{
    int temp = n;
    while (temp > 0)
    {
         
        // Getting the last digit
        int last_digit = temp % 10;
         
        // Every number is divisible
        // by 1 and dividing a number
        // by 0 isn't possible. Thus
        // numbers with 0 as a digit
        // must be discarded.
        if (last_digit == 0 ||
            last_digit == 1)
            return false;
             
        // If any digit divides the
        // number, return false
        if (n % last_digit == 0)
            return false;
        temp = temp / 10;
    }
     
    // If no digit divides the
    // number, return true;
    return true;
}
 
// Function to find the smallest
// number not divisible by any
// of its digits.
static void solve(int n)
{
     
    // Get the lower range of n
    // digit number
    int L = power(10, n - 1);
     
    // Get the high range of n
    // digit number
    int R = power(10, n) - 1;
     
    int flag = 0;
     
    // Check all the N-digit numbers
    for(int i = L; i <= R; i++)
    {
        boolean answer = check(i);
         
        // If the first number to satify
        // the constraints is found
        // print it, set the flag value
        // and break out of the loop.
        if (answer == true)
        {
            System.out.println(i);
            flag++;
            break;
        }
    }
     
    // If no such digit found,
    // return -1 as per problem statement
    if (flag == 0)
    System.out.println("-1");
}
 
// Driver code
public static void main(String[] args)
{
    int N = 4;
     
    solve(N);
}
}
 
// This code is contributed by offbeat

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Python3

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# Python3 Program for the
# given problem
 
# Function to calculate
# power
def power(a, b):
 
    if (b == 0):
        return 1;
    if (b == 1):
        return a;
  
    tmp = power(a, b // 2); 
    result = tmp * tmp;
  
    if (b % 2 == 1):
        result *= a;
  
    return result;
 
# Function to check if the
# N-digit number satifies the
# given condition or not
def check(n):
 
    temp = n;
    while (temp > 0):
  
        # Getting the last digit
        last_digit = temp % 10;
  
        # Every number is divisible
        # by 1 and dividing a number
        # by 0 isn't possible. Thus
        # numbers with 0 as a digit
        # must be discarded.
        if (last_digit == 0 or
            last_digit == 1):
            return False;
  
        # If any digit divides the
        # number, return false
        if (n % last_digit == 0):
            return False;
             
        temp = temp // 10;    
  
    # If no digit divides the
    # number, return true;
    return True;
 
# Function to find the smallest
# number not divisible by any
# of its digits.
def solve(n):
 
    # Get the lower range of n
    # digit number
    L = power(10, n - 1);
  
    # Get the high range of n
    # digit number
    R = power(10, n) - 1;
  
    flag = 0;
  
    # check all the N-digit
    # numbers
    for i in range(L, R + 1):
        answer = check(i);
  
        # If the first number to satify
        # the constraints is found
        # print it, set the flag value
        # and break out of the loop.
        if (answer):           
            print(i)
            flag += 1;
            break;
         
    # If no such digit found,
    # return -1 as per problem
    # statement
    if (flag == 0):
        print(-1)
         
# Driver code
if __name__ == "__main__":
     
    N = 4;
    solve(N);
 
# This code is contributed by rutvik_56

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C#

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// C# program for the given problem
using System;
 
class GFG{
     
// Function to calculate power
static int power(int a, int b)
{
    if (b == 0)
        return 1;
    if (b == 1)
        return a;
         
    int tmp = power(a, b / 2);
    int result = tmp * tmp;
     
    if (b % 2 == 1)
        result *= a;
 
    return result;
}
 
// Function to check if the
// N-digit number satifies the
// given condition or not
static bool check(int n)
{
    int temp = n;
    while (temp > 0)
    {
         
        // Getting the last digit
        int last_digit = temp % 10;
         
        // Every number is divisible
        // by 1 and dividing a number
        // by 0 isn't possible. Thus
        // numbers with 0 as a digit
        // must be discarded.
        if (last_digit == 0 ||
            last_digit == 1)
            return false;
             
        // If any digit divides the
        // number, return false
        if (n % last_digit == 0)
            return false;
        temp = temp / 10;
    }
     
    // If no digit divides the
    // number, return true;
    return true;
}
 
// Function to find the smallest
// number not divisible by any
// of its digits.
static void solve(int n)
{
     
    // Get the lower range of n
    // digit number
    int L = power(10, n - 1);
     
    // Get the high range of n
    // digit number
    int R = power(10, n) - 1;
     
    int flag = 0;
     
    // Check all the N-digit numbers
    for(int i = L; i <= R; i++)
    {
        bool answer = check(i);
         
        // If the first number to satify
        // the constraints is found
        // print it, set the flag value
        // and break out of the loop.
        if (answer == true)
        {
            Console.WriteLine(i);
            flag++;
            break;
        }
    }
     
    // If no such digit found,
    // return -1 as per problem statement
    if (flag == 0)
    Console.WriteLine("-1");
}
 
// Driver code
public static void Main(String[] args)
{
    int N = 4;
     
    solve(N);
}
}
 
// This code is contributed by 29AjayKumar

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Output: 

2227

 

Time Complexity: O(N) 
Auxiliary Space: O(1)
 

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