# Find the Nth natural number which is not divisible by A

Given two integers A and N, our task is to find the Nth natural number which is not divisible by A.

Examples:

Input: A = 4, N = 12
Output: 15
Explanation:
The series starting from 1 excluding the multiples of A would be 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17 and the 12th term which is not divisible by 4 is 15.

Input: A = 3, N = 20
Output: 29
Explanation:
The series starting from 1 excluding the multiples of A would be 1, 2, 4, 5, 7, 8, 10, 11 and so on and the Nth number which is not divisible by 3 is 29.

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

Approach:

To solve the problem mentioned above we have to observe that there is a gap after every (A – 1) integer as the multiples of A are skipped. To find that the number N lies in which set we divide N by (A – 1), and store it in a variable lets say quotient. Now multiplying A with that variable and adding the remainder to it we will get the resultant answer.

```If A = 4, N = 7:
quotient = 7 / 3 = 2
remainder = 7 % 3 = 1

(A * quotient) + remainder
= 4 * 2 + 1 = 9
```

But if the remainder is 0 it means it is the last element in the set. Lets us understand it by an example.

```If A = 4, N = 6:
quotient = 6 / 3 = 2
remainder = 6 % 3 = 0

(A * quotient) - 1
= 4 * 2 - 1 = 7
```

Below is the implementation of the above approach:

 `// C++ code to Find the Nth number which ` `// is not divisible by A from the series ` `#include ` `using` `namespace` `std; ` ` `  `void` `findNum(``int` `n, ``int` `k) ` `{ ` `     `  `    ``// Find the quotient and the remainder ` `    ``// when k is divided by n-1 ` `    ``int` `q = k / (n - 1); ` `    ``int` `r = k % (n - 1); ` `    ``int` `a; ` ` `  `    ``// If the remainder is not 0 ` `    ``// multiply n by q and subtract 1 ` `    ``// if remainder is 0 then ` `    ``// multiply n by q ` `    ``// and add the remainder ` `    ``if``(r != 0) ` `       ``a = (n * q) + r; ` `    ``else` `       ``a = (n * q) - 1; ` ` `  `    ``// Print the answer ` `    ``cout << a; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `A = 4, N = 6; ` `     `  `    ``findNum(A, N); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by PratikBasu `

 `// Java code to Find the Nth number which ` `// is not divisible by A from the series ` `class` `GFG { ` `     `  `static` `void` `findNum(``int` `n, ``int` `k) ` `{ ` ` `  `    ``// Find the quotient and the remainder ` `    ``// when k is divided by n-1 ` `    ``int` `q = k / (n - ``1``); ` `    ``int` `r = k % (n - ``1``); ` `    ``int` `a = ``0``; ` `     `  `    ``// If the remainder is not 0 ` `    ``// multiply n by q and subtract 1 ` `    ``// if remainder is 0 then ` `    ``// multiply n by q ` `    ``// and add the remainder ` `    ``if` `(r != ``0``) ` `        ``a = (n * q) + r; ` `    ``else` `        ``a = (n * q) - ``1``; ` ` `  `    ``// Print the answer ` `    ``System.out.println(a); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `A = ``4``; ` `    ``int` `N = ``6``; ` ` `  `    ``findNum(A, N); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

 `# Python3 code to Find the Nth number which ` `# is not divisible by A from the series ` ` `  `def` `findNum(n, k): ` `     `  `    ``# Find the quotient and the remainder ` `    ``# when k is divided by n-1 ` `    ``q ``=` `k``/``/``(n``-``1``) ` `    ``r ``=` `k ``%` `(n``-``1``) ` `     `  `    ``# if the remainder is not 0  ` `    ``# multiply n by q and subtract 1 ` `     `  `    ``# if remainder is 0 then  ` `    ``# multiply n by q  ` `    ``# and add the remainder ` `    ``if``(r !``=` `0``): ` `        ``a ``=` `(n ``*` `q)``+``r ` `    ``else``: ` `        ``a ``=` `(n ``*` `q)``-``1` `         `  `    ``# print the answer ` `    ``print``(a) ` ` `  `# driver code ` `A ``=` `4` `N ``=` `6` `findNum(A, N) `

 `// C# code to find the Nth number which ` `// is not divisible by A from the series ` `using` `System; ` ` `  `class` `GFG{ ` `     `  `static` `void` `findNum(``int` `n, ``int` `k) ` `{ ` ` `  `    ``// Find the quotient and the remainder ` `    ``// when k is divided by n-1 ` `    ``int` `q = k / (n - 1); ` `    ``int` `r = k % (n - 1); ` `    ``int` `a = 0; ` `     `  `    ``// If the remainder is not 0 ` `    ``// multiply n by q and subtract 1 ` `    ``// if remainder is 0 then ` `    ``// multiply n by q ` `    ``// and add the remainder ` `    ``if` `(r != 0) ` `        ``a = (n * q) + r; ` `    ``else` `        ``a = (n * q) - 1; ` ` `  `    ``// Print the answer ` `    ``Console.WriteLine(a); ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `A = 4; ` `    ``int` `N = 6; ` ` `  `    ``findNum(A, N); ` `} ` `} ` ` `  `// This code is contributed by amal kumar choubey `

Output:
```7
```

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