Find the largest N digit multiple of N

Given a number **N**, the task is to find the largest **N-digit multiple of N**.

**Examples:**

Input:N = 2

Output:98

Explanation:

98 is the largest multiple of 2 and is of 2 digits.

Input:N = 3

Output:999

Explanation:

999 is the largest multiple of 3 and is of 3 digits.

**Approach:** The idea is to make an observation.

- If we observe carefully, a series will be formed as 9, 98, 999, 9996, 99995, …
- In the above series, the N-th term can be calculated as:

- Therefore, the number N is taken as the input and the above formula is implemented.

Below is the implementation of the above approach:

## C++

`// C++ program to find largest multiple ` `// of N containing N digits ` `#include <iostream> ` `#include <math.h> ` `using` `namespace` `std; ` ` ` `// Function to find the largest ` `// N digit multiple of N ` ` ` `void` `smallestNumber(` `int` `N) ` `{ ` ` ` `cout << N * ` `floor` `((` `pow` `(10, N) - 1) / N); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `N = 2; ` ` ` `smallestNumber(N); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find largest multiple ` `// of N containing N digits ` `import` `java.util.*; ` `class` `GFG{ ` ` ` `// Function to find the largest ` `// N digit multiple of N ` `static` `void` `smallestNumber(` `int` `N) ` `{ ` ` ` `System.out.print(N * Math.floor(( ` ` ` `Math.pow(` `10` `, N) - ` `1` `) / N)); ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String args[]) ` `{ ` ` ` `int` `N = ` `2` `; ` ` ` `smallestNumber(N); ` `} ` `} ` ` ` `// This code is contributed by Nidhi_biet ` |

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## Python3

`# Python3 program to find largest multiple ` `# of N containing N digits ` `from` `math ` `import` `floor ` ` ` `# Function to find the largest ` `# N digit multiple of N ` `def` `smallestNumber(N): ` ` ` `print` `(N ` `*` `floor((` `pow` `(` `10` `, N) ` `-` `1` `) ` `/` `N)) ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` `N ` `=` `2` ` ` `smallestNumber(N) ` ` ` `# This code is contributed by Mohit Kumar ` |

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## C#

`// C# program to find largest multiple ` `// of N containing N digits ` `using` `System; ` `class` `GFG{ ` ` ` `// Function to find the largest ` `// N digit multiple of N ` `static` `void` `smallestNumber(` `int` `N) ` `{ ` ` ` `Console.Write(N * Math.Floor(( ` ` ` `Math.Pow(10, N) - 1) / N)); ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `N = 2; ` ` ` `smallestNumber(N); ` `} ` `} ` ` ` `// This code is contributed by Code_Mech ` |

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**Output:**

98

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