# Divide the two given numbers by their common divisors

Given two numbers A and B, the task is to Divide the two numbers A and B by their common divisors. The numbers A and B is less than 10^8.**Examples:**

Input:A = 10, B = 15Output:A = 2, B = 3 The common factors are 1, 5Input:A = 100, B = 150Output:A = 2, B = 3

**Naive Approach:** Iterate from i = 1 to minimum of A and B and check whether **i** is a factor of both A and B. If **i** is a factor of **A** and **B** then Divide the two numbers A and B by i.

Below is the implementation of the above approach:

## C++

`// C++ implementation of above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// print the numbers after dividing` `// them by their common factors` `void` `divide(` `int` `a, ` `int` `b)` `{` ` ` `// iterate from 1 to minimum of a and b` ` ` `for` `(` `int` `i = 2; i <= min(a, b); i++) {` ` ` `// if i is the common factor` ` ` `// of both the numbers` ` ` `while` `(a % i == 0 && b % i == 0) {` ` ` `a = a / i;` ` ` `b = b / i;` ` ` `}` ` ` `}` ` ` `cout << ` `"A = "` `<< a << ` `", B = "` `<< b << endl;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `A = 10, B = 15;` ` ` `// divide A and B by their common factors` ` ` `divide(A, B);` ` ` `return` `0;` `}` |

## C

`// C implementation of above approach` `#include <stdio.h>` `// print the numbers after dividing` `// them by their common factors` `void` `divide(` `int` `a, ` `int` `b)` `{` ` ` `// iterate from 1 to minimum of a and b` ` ` `int` `min;` ` ` `min = a;` ` ` `if` `(min > b)` ` ` `min = b;` ` ` `for` `(` `int` `i = 2; i <= min; i++) {` ` ` `// if i is the common factor` ` ` `// of both the numbers` ` ` `while` `(a % i == 0 && b % i == 0) {` ` ` `a = a / i;` ` ` `b = b / i;` ` ` `}` ` ` `}` ` ` `printf` `(` `"A = %d, B = %d\n"` `, a, b);` `}` `// Driver code` `int` `main()` `{` ` ` `int` `A = 10, B = 15;` ` ` `// divide A and B by their common factors` ` ` `divide(A, B);` ` ` `return` `0;` `}` `// This code is contributed by kothvvsakash` |

## Java

`// Java implementation of above approach` `import` `java.util.*;` `class` `solution` `{` `// print the numbers after dividing` `// them by their common factors` `static` `void` `divide(` `int` `a, ` `int` `b)` `{` ` ` `// iterate from 1 to minimum of a and b` ` ` `for` `(` `int` `i = ` `2` `; i <= Math.min(a, b); i++) {` ` ` `// if i is the common factor` ` ` `// of both the numbers` ` ` `while` `(a % i == ` `0` `&& b % i == ` `0` `) {` ` ` `a = a / i;` ` ` `b = b / i;` ` ` `}` ` ` `}` ` ` `System.out.println(` `"A = "` `+a+` `", B = "` `+b);` `}` `// Driver code` `public` `static` `void` `main(String args[])` `{` ` ` `int` `A = ` `10` `, B = ` `15` `;` ` ` `// divide A and B by their common factors` ` ` `divide(A, B);` `}` `}` `// This code is contributed by` `// Surendra_Gangwar` |

## Python3

`# Python3 implementation of above approach` `# print the numbers after dividing` `# them by their common factors` `def` `divide(a, b) :` ` ` ` ` `# iterate from 1 to minimum of a and b` ` ` `for` `i ` `in` `range` `(` `2` `, ` `min` `(a, b) ` `+` `1` `) :` ` ` `# if i is the common factor` ` ` `# of both the numbers` ` ` `while` `(a ` `%` `i ` `=` `=` `0` `and` `b ` `%` `i ` `=` `=` `0` `) :` ` ` `a ` `=` `a ` `/` `/` `i` ` ` `b ` `=` `b ` `/` `/` `i` ` ` `print` `(` `"A ="` `, a, ` `", B ="` `, b)` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `A, B ` `=` `10` `, ` `15` ` ` `# divide A and B by their` ` ` `# common factors` ` ` `divide(A, B)` ` ` `# This code is contributed by Ryuga` |

## C#

`// C# implementation of above approach` `using` `System;` `class` `GFG` `{` ` ` `// print the numbers after dividing` `// them by their common factors` `static` `void` `divide(` `int` `a, ` `int` `b)` `{` ` ` `// iterate from 1 to minimum of a and b` ` ` `for` `(` `int` `i = 2; i <= Math.Min(a, b); i++)` ` ` `{` ` ` `// if i is the common factor` ` ` `// of both the numbers` ` ` `while` `(a % i == 0 && b % i == 0)` ` ` `{` ` ` `a = a / i;` ` ` `b = b / i;` ` ` `}` ` ` `}` ` ` `Console.WriteLine(` `"A = "` `+a+` `", B = "` `+b);` `}` `// Driver code` `static` `public` `void` `Main ()` `{` ` ` `int` `A = 10, B = 15;` ` ` `// divide A and B by their common factors` ` ` `divide(A, B);` `}` `}` `// This code is contributed by ajit.` |

## PHP

`<?php` `// PHP implementation of above approach` `// print the numbers after dividing` `// them by their common factors` `function` `divide(` `$a` `, ` `$b` `)` `{` ` ` `// iterate from 1 to minimum of a and b` ` ` `for` `(` `$i` `= 2; ` `$i` `<= min(` `$a` `, ` `$b` `); ` `$i` `++)` ` ` `{` ` ` `// if i is the common factor` ` ` `// of both the numbers` ` ` `while` `(` `$a` `% ` `$i` `== 0 &&` ` ` `$b` `% ` `$i` `== 0)` ` ` `{` ` ` `$a` `= ` `$a` `/ ` `$i` `;` ` ` `$b` `= ` `$b` `/ ` `$i` `;` ` ` `}` ` ` `}` ` ` `echo` `"A = "` `, ` `$a` `, ` `", B = "` `, ` `$b` `, ` `"\n"` `;` `}` `// Driver code` `$A` `= 10;` `$B` `= 15;` `// divide A and B by their common factors` `divide(` `$A` `, ` `$B` `);` `// This code is contributed by Sach_Code` `?>` |

## Javascript

`<script>` `// Javascript implementation of above approach` `// print the numbers after dividing` `// them by their common factors` `function` `divide(a, b)` `{` ` ` `// iterate from 1 to minimum of a and b` ` ` `for` `(let i = 2; i <= Math.min(a, b); i++) {` ` ` `// if i is the common factor` ` ` `// of both the numbers` ` ` `while` `(a % i == 0 && b % i == 0) {` ` ` `a = a / i;` ` ` `b = b / i;` ` ` `}` ` ` `}` ` ` `document.write(` `"A = "` `+ a + ` `", B = "` `+ b + ` `"<br>"` `);` `}` `// Driver code` ` ` `let A = 10, B = 15;` ` ` `// divide A and B by their common factors` ` ` `divide(A, B);` `// This code is contributed by Mayank Tyagi` `</script>` |

**Output:**

A = 2, B = 3

An **efficient approach **is to use the same concept used in Common divisors of two numbers. Calculate the greatest common divisor (gcd) of given two numbers, and then divide the numbers by their gcd.

## C++

`// C++ implementation of above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to calculate gcd of two numbers` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` `}` `// Function to calculate all common divisors` `// of two given numbers` `// a, b --> input integer numbers` `void` `commDiv(` `int` `a, ` `int` `b)` `{` ` ` `// find gcd of a, b` ` ` `int` `n = gcd(a, b);` ` ` `a = a / n;` ` ` `b = b / n;` ` ` `cout << ` `"A = "` `<< a << ` `", B = "` `<< b << endl;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a = 10, b = 15;` ` ` `commDiv(a, b);` ` ` `return` `0;` `}` |

## C

`// C implementation of above approach` `#include <stdio.h>` `// Function to calculate gcd of two numbers` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` `}` `// Function to calculate all common divisors` `// of two given numbers` `// a, b --> input integer numbers` `void` `commDiv(` `int` `a, ` `int` `b)` `{` ` ` `// find gcd of a, b` ` ` `int` `n = gcd(a, b);` ` ` `a = a / n;` ` ` `b = b / n;` ` ` ` ` `printf` `(` `"A = %d, B = %d\n"` `,a,b);` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a = 10, b = 15;` ` ` `commDiv(a, b);` ` ` `return` `0;` `}` `// This code is contributed by kothvvsaakash` |

## Java

`// Java implementation of above approach` `class` `GFG` `{` ` ` `// Function to calculate gcd` `// of two numbers` `static` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == ` `0` `)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` `}` `// Function to calculate all common` `// divisors of two given numbers` `// a, b --> input integer numbers` `static` `void` `commDiv(` `int` `a, ` `int` `b)` `{` ` ` `// find gcd of a, b` ` ` `int` `n = gcd(a, b);` ` ` `a = a / n;` ` ` `b = b / n;` ` ` `System.out.println(` `"A = "` `+ a +` ` ` `", B = "` `+ b);` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `a = ` `10` `, b = ` `15` `;` ` ` `commDiv(a, b);` `}` `}` `// This code is contributed` `// by Code_Mech` |

## Python3

`# Python3 implementation of above approach` `# Function to calculate gcd of two numbers` `def` `gcd(a, b):` ` ` `if` `(a ` `=` `=` `0` `):` ` ` `return` `b` ` ` `return` `gcd(b ` `%` `a, a)` `# Function to calculate all common` `# divisors of two given numbers` `# a, b --> input eger numbers` `def` `commDiv(a, b):` ` ` ` ` `# find gcd of a, b` ` ` `n ` `=` `gcd(a, b)` ` ` `a ` `=` `a ` `/` `/` `n` ` ` `b ` `=` `b ` `/` `/` `n` ` ` `print` `(` `"A ="` `, a, ` `", B ="` `, b)` `# Driver code` `a, b ` `=` `10` `, ` `15` `commDiv(a, b)` `# This code is contributed` `# by mohit kumar` |

## C#

`// C# implementation of above approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to calculate gcd` `// of two numbers` `static` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` `}` `// Function to calculate all common` `// divisors of two given numbers` `// a, b --> input integer numbers` `static` `void` `commDiv(` `int` `a, ` `int` `b)` `{` ` ` `// find gcd of a, b` ` ` `int` `n = gcd(a, b);` ` ` `a = a / n;` ` ` `b = b / n;` ` ` `Console.WriteLine(` `"A = "` `+ a +` ` ` `", B = "` `+ b);` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `a = 10, b = 15;` ` ` `commDiv(a, b);` `}` `}` `// This code is contributed` `// by Code_Mech` |

## PHP

`<?php` `// PHP implementation of above approach` `// Function to calculate gcd of` `// two numbers` `function` `gcd(` `$a` `, ` `$b` `)` `{` ` ` `if` `(` `$a` `== 0)` ` ` `return` `$b` `;` ` ` `return` `gcd(` `$b` `% ` `$a` `, ` `$a` `);` `}` `// Function to calculate all common` `// divisors of two given numbers` `// a, b --> input integer numbers` `function` `commDiv(` `$a` `, ` `$b` `)` `{` ` ` `// find gcd of a, b` ` ` `$n` `= gcd(` `$a` `, ` `$b` `);` ` ` `$a` `= (int)(` `$a` `/ ` `$n` `);` ` ` `$b` `= (int)(` `$b` `/ ` `$n` `);` ` ` `echo` `"A = "` `. ` `$a` `.` ` ` `", B = "` `. ` `$b` `. ` `"\n"` `;` `}` `// Driver code` `$a` `= 10;` `$b` `= 15;` `commDiv(` `$a` `, ` `$b` `);` `// This code is contributed by mits` `?>` |

## Javascript

`<script>` ` ` `// Javascript implementation of above approach` ` ` ` ` `// Function to calculate gcd` ` ` `// of two numbers` ` ` `function` `gcd(a, b)` ` ` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` `// Function to calculate all common` ` ` `// divisors of two given numbers` ` ` `// a, b --> input integer numbers` ` ` `function` `commDiv(a, b)` ` ` `{` ` ` `// find gcd of a, b` ` ` `let n = gcd(a, b);` ` ` `a = parseInt(a / n, 10);` ` ` `b = parseInt(b / n, 10);` ` ` `document.write(` `"A = "` `+ a + ` `", B = "` `+ b);` ` ` `}` ` ` ` ` `let a = 10, b = 15;` ` ` `commDiv(a, b);` ` ` `</script>` |

**Output:**

A = 2, B = 3

**Time complexity : **O(n)