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; ` `} ` |

## 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. ` `?> ` |

**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.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Sum of Areas of Rectangles possible for an array
- Array with GCD of any of its subset belongs to the given array
- Count number of pairs (A <= N, B <= N) such that gcd (A , B) is B
- Number Theory (Interesting Facts and Algorithms)
- Print the kth common factor of two numbers
- Program to implement Collatz Conjecture
- Count natural numbers whose factorials are divisible by x but not y
- Stein's Algorithm for finding GCD
- GCD of two numbers when one of them can be very large
- LCM of given array elements
- Find all divisors of a natural number | Set 2
- Pollard's Rho Algorithm for Prime Factorization
- Euclidean algorithms (Basic and Extended)
- Program to find LCM of two numbers
- Efficient program to print all prime factors of a given number