# GCD of two numbers formed by n repeating x and y times

Given three positive integer **n**, **x**, **y**. The task is to print Greatest Common Divisor of numbers formed by n repeating x times and number formed by n repeating y times.

0 <= n, x, y <= 1000000000.**Examples :**

Input : n = 123, x = 2, y = 3. Output : 123 Number formed are 123123 and 123123123. Greatest Common Divisor of 123123 and 123123123 is 123. Input : n = 4, x = 4, y = 6. Output : 44

The idea is based on Euclidean algorithm to compute GCD of two number.

Let f(n, x) be a function which gives a number n repeated x times. So, we need to find GCD(f(n, x), f(n, y)).

Let n = 123, x = 3, y = 2.

So, first number A is f(123, 3) = 123123123 and second number B is f(123, 2) = 123123. We know, GCD(A,B) = GCD(A – B, B), using this property we can subtract any multiple of B, say B’ from first A as long as B’ is smaller than A.

So, A = 123123123 and B’ can be 123123000. On subtracting A will became 123 and B remains same.

Therefore, A = A – B’ = f(n, x – y).

So, GCD(f(n, x), f(n, y)) = GCD(f(n, x – y), f(n, y))

We can conclude following,

GCD(f(n, x), f(n, y)) = f(n, GCD(x, y)).

Below is the implementation based on this approach:

## CPP

`// C++ program to print Greatest Common Divisor` `// of number formed by N repeating x times and` `// y times.` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Return the Greatest common Divisor of two numbers.` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b%a, a);` `}` `// Prints Greatest Common Divisor of number formed` `// by n repeating x times and y times.` `void` `findgcd(` `int` `n, ` `int` `x, ` `int` `y)` `{` ` ` `// Finding GCD of x and y.` ` ` `int` `g = gcd(x,y);` ` ` `// Print n, g times.` ` ` `for` `(` `int` `i = 0; i < g; i++)` ` ` `cout << n;` `}` `// Driven Program` `int` `main()` `{` ` ` `int` `n = 123, x = 5, y = 2;` ` ` `findgcd(n, x, y);` ` ` `return` `0;` `}` |

## Java

`// Java program to print Greatest Common Divisor` `// of number formed by N repeating x times and` `// y times` `class` `GFG {` ` ` ` ` `// Return the Greatest common Divisor` ` ` `// of two numbers.` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b) {` ` ` ` ` `if` `(a == ` `0` `)` ` ` `return` `b;` ` ` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` ` ` `// Prints Greatest Common Divisor of` ` ` `// number formed by n repeating x` ` ` `// times and y times.` ` ` `static` `void` `findgcd(` `int` `n, ` `int` `x, ` `int` `y) {` ` ` ` ` `// Finding GCD of x and y.` ` ` `int` `g = gcd(x, y);` ` ` ` ` `// Print n, g times.` ` ` `for` `(` `int` `i = ` `0` `; i < g; i++)` ` ` `System.out.print(n);` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args) {` ` ` ` ` `int` `n = ` `123` `, x = ` `5` `, y = ` `2` `;` ` ` `findgcd(n, x, y);` ` ` `}` `}` `// This code is contributed by Anant Agarwal.` |

## Python3

`# Python program to print Greatest` `# Common Divisor of number formed` `# by N repeating x times and y times` `# Return the Greatest common Divisor` `# of two numbers.` `def` `gcd(a, b):` ` ` ` ` `if` `(a ` `=` `=` `0` `):` ` ` `return` `b` ` ` ` ` `return` `gcd(b ` `%` `a, a)` `# Prints Greatest Common Divisor of` `# number formed by n repeating x times` `# and y times.` `def` `findgcd(n, x, y):` ` ` `# Finding GCD of x and y.` ` ` `g ` `=` `gcd(x, y)` ` ` `# Print n, g times.` ` ` `for` `i ` `in` `range` `(g):` ` ` `print` `(n)` `# Driver code` `n ` `=` `123` `x ` `=` `5` `y ` `=` `2` `findgcd(n, x, y)` `# This code is contributed by Anant Agarwal.` |

## C#

`// C# program to print Greatest Common` `// Divisor of number formed by N` `// repeating x times and y times` `using` `System;` `class` `GFG {` ` ` ` ` `// Return the Greatest common` ` ` `// Divisor of two numbers.` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` ` ` `return` `gcd(b % a, a);` ` ` `}` ` ` ` ` `// Prints Greatest Common` ` ` `// Divisor of number formed` ` ` `// by n repeating x times` ` ` `// and y times.` ` ` `static` `void` `findgcd(` `int` `n,` ` ` `int` `x, ` `int` `y)` ` ` `{` ` ` ` ` `// Finding GCD of x and y.` ` ` `int` `g = gcd(x, y);` ` ` ` ` `// Print n, g times.` ` ` `for` `(` `int` `i = 0; i < g; i++)` ` ` `Console.Write(n);` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `Main() {` ` ` ` ` `int` `n = 123, x = 5, y = 2;` ` ` ` ` `findgcd(n, x, y);` ` ` `}` `}` `// This code is contributed by` `// nitin mittal.` |

## PHP

`<?php` `// PHP program to print` `// Greatest Common Divisor` `// of number formed by N` `// repeating x times and y times.` `// Return the Greatest common` `// Divisor of two numbers.` `function` `gcd(` `$a` `, ` `$b` `)` `{` ` ` `if` `(` `$a` `== 0)` ` ` `return` `$b` `;` ` ` `return` `gcd(` `$b` `% ` `$a` `, ` `$a` `);` `}` `// Prints Greatest Common Divisor` `// of number formed by n repeating` `// x times and y times.` `function` `findgcd(` `$n` `, ` `$x` `, ` `$y` `)` `{` ` ` `// Finding GCD of x and y.` ` ` `$g` `= gcd(` `$x` `, ` `$y` `);` ` ` `// Print n, g times.` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$g` `; ` `$i` `++)` ` ` `echo` `(` `$n` `);` `}` `// Driver Code` `$n` `= 123; ` `$x` `= 5; ` `$y` `= 2;` `findgcd(` `$n` `, ` `$x` `, ` `$y` `);` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// Javascript program to print Greatest Common Divisor` `// of number formed by N repeating x times and` `// y times.` `// Return the Greatest common Divisor of two numbers.` `function` `gcd(a, b)` `{` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `return` `gcd(b%a, a);` `}` `// Prints Greatest Common Divisor of number formed` `// by n repeating x times and y times.` `function` `findgcd(n, x, y)` `{` ` ` `// Finding GCD of x and y.` ` ` `let g = gcd(x,y);` ` ` `// Print n, g times.` ` ` `for` `(let i = 0; i < g; i++)` ` ` `document.write(n);` `}` `// Driven Program` ` ` `let n = 123, x = 5, y = 2;` ` ` `findgcd(n, x, y);` ` ` `// This is code is contributed by Mayank Tyagi` `</script>` |

**Output :**

123

**Time Complexity: **O(log(min(n)) ) **Auxiliary Space:** O(log(min(n))

This article is contributed by **Aarti_Rathi** and **Anuj Chauhan**. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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