# Count of m digit integers that are divisible by an integer n

Given two numbers m and n, count number of m digit numbers that are divisible by n.

Examples:

Input : m = 2 n = 6 Output : 15 Two digit numbers that are divisible by 6 are 12, 18, 24, 30, 36, ....., 96. Input : m = 3 n = 5 Output :180

A **simple solution** is two try all m digit numbers. For every number, check if it is divisible by n. If yes, we increment count.

An **efficient solution** involves following steps.

The idea is based on the fact that starting from first divisible number, every n-th number is divisible by n.

- Find largest m digit number.
- Find largest m-1 digit number.
- Divide both number by n and subtract later from prior.

Below is the implementation of above steps.

## C++

`// C++ program to count m digit numbers having ` `// n as divisor. ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Returns count of m digit numbers having n ` `// as divisor ` `int` `findCount(` `int` `m, ` `int` `n) ` `{ ` ` ` `// generating largest number of m digit ` ` ` `int` `num1 = 0; ` ` ` `for` `(` `int` `i = 0; i < m; i++) ` ` ` `num1 = (num1 * 10) + 9; ` ` ` ` ` `// generating largest number of m-1 digit ` ` ` `int` `num2 = 0; ` ` ` `for` `(` `int` `i = 0; i < (m - 1); i++) ` ` ` `num2 = (num2 * 10) + 9; ` ` ` ` ` `// returning number of dividend ` ` ` `return` `((num1 / n) - (num2 / n)); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `m = 2, n = 6; ` ` ` `printf` `(` `"%d\n"` `, findCount(m, n)); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count m digit numbers having ` `// n as divisor. ` ` ` `class` `Main ` `{ ` ` ` `// Returns count of m digit numbers having n ` ` ` `// as divisor ` ` ` `static` `int` `findCount(` `int` `m, ` `int` `n) ` ` ` `{ ` ` ` `// generating largest number of m digit ` ` ` `int` `num1 = ` `0` `; ` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++) ` ` ` `num1 = (num1 * ` `10` `) + ` `9` `; ` ` ` ` ` `// generating largest number of m-1 digit ` ` ` `int` `num2 = ` `0` `; ` ` ` `for` `(` `int` `i = ` `0` `; i < (m - ` `1` `); i++) ` ` ` `num2 = (num2 * ` `10` `) + ` `9` `; ` ` ` ` ` `// returning number of dividend ` ` ` `return` `((num1 / n) - (num2 / n)); ` ` ` `} ` ` ` ` ` `// main function ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `int` `m = ` `2` `, n = ` `6` `; ` ` ` `System.out.println(findCount(m, n)); ` ` ` `} ` `} ` ` ` `/* This code is contributed by Harsh Agarwal */` |

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## Python3

`# Python3 program to count m digit ` `# numbers having n as divisor. ` ` ` `# Returns count of m digit ` `# numbers having n as divisor ` `def` `findCount(m, n): ` ` ` ` ` `# Generating largest number of m digit ` ` ` `num1 ` `=` `0` ` ` ` ` `for` `i ` `in` `range` `(` `0` `, m): ` ` ` `num1 ` `=` `(num1 ` `*` `10` `) ` `+` `9` ` ` ` ` `# Generating largest number of m-1 digit ` ` ` `num2 ` `=` `0` ` ` ` ` `for` `i ` `in` `range` `(` `0` `, (m ` `-` `1` `)): ` ` ` `num2 ` `=` `(num2 ` `*` `10` `) ` `+` `9` ` ` ` ` `# returning number of dividend ` ` ` `return` `int` `((num1 ` `/` `n) ` `-` `(num2 ` `/` `n)) ` ` ` ` ` `# Driver code ` `m ` `=` `2` `; n ` `=` `6` `print` `(findCount(m, n)) ` ` ` `# This code is contributed by Smitha Dinesh Semwal ` |

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## C#

`// C# program to count m digit numbers ` `// having n as divisor. ` `using` `System; ` ` ` `class` `GfG { ` ` ` ` ` `// Returns count of m digit numbers ` ` ` `// having n as divisor ` ` ` `static` `int` `findCount(` `int` `m, ` `int` `n) ` ` ` `{ ` ` ` ` ` `// generating largest number ` ` ` `// of m digit ` ` ` `int` `num1 = 0; ` ` ` `for` `(` `int` `i = 0; i < m; i++) ` ` ` `num1 = (num1 * 10) + 9; ` ` ` ` ` `// generating largest number ` ` ` `// of m-1 digit ` ` ` `int` `num2 = 0; ` ` ` `for` `(` `int` `i = 0; i < (m - 1); i++) ` ` ` `num2 = (num2 * 10) + 9; ` ` ` ` ` `// returning number of dividend ` ` ` `return` `((num1 / n) - (num2 / n)); ` ` ` `} ` ` ` ` ` `// main function ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `int` `m = 2, n = 6; ` ` ` ` ` `Console.Write(findCount(m, n)); ` ` ` `} ` `} ` ` ` `// This code is contributed by parashar. ` |

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## PHP

`<?php ` `// PHP program to count m digit ` `// numbers having n as divisor. ` ` ` `// Returns count of m digit numbers ` `// having n as divisor ` `function` `findCount(` `$m` `, ` `$n` `) ` `{ ` ` ` `// generating largest number ` ` ` `// of m digit ` ` ` `$num1` `= 0; ` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$m` `; ` `$i` `++) ` ` ` `$num1` `= (` `$num1` `* 10) + 9; ` ` ` ` ` `// generating largest number ` ` ` `// of m-1 digit ` ` ` `$num2` `= 0; ` ` ` `for` `(` `$i` `= 0; ` `$i` `< (` `$m` `- 1); ` `$i` `++) ` ` ` `$num2` `= (` `$num2` `* 10) + 9; ` ` ` ` ` `// returning number of dividend ` ` ` `return` `((` `$num1` `/ ` `$n` `) - (` `$num2` `/ ` `$n` `)); ` `} ` ` ` `// Driver code ` `$m` `= 2; ` `$n` `= 6; ` `echo` `findCount(` `$m` `, ` `$n` `), ` `"\n"` `; ` ` ` `// This code is contributed by ajit ` `?> ` |

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Output :

15

Time complexity : O(m)

This article is contributed by Aditya Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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