# 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 substract 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 substracting A will became 123 and B remains same.

Therfore, 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; ` `} ` |

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## 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. ` |

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## 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. ` |

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## 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. ` |

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## 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. ` `?> ` |

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**Output :**

123

This article is contributed by **Anuj Chauhan**. 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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