# 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; ` `} ` |

*chevron_right*

*filter_none*

## 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. ` |

*chevron_right*

*filter_none*

## 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. ` |

*chevron_right*

*filter_none*

## 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. ` |

*chevron_right*

*filter_none*

## 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. ` `?> ` |

*chevron_right*

*filter_none*

**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 sum of all subsets of a set formed by first N natural numbers
- Maximum factors formed by two numbers
- Sum of all subsets of a set formed by first n natural numbers
- Minimum sum of two numbers formed from digits of an array
- N digit numbers divisible by 5 formed from the M digits
- Count numbers formed by given two digit with sum having given digits
- Find the count of numbers that can be formed using digits 3, 4 only and having length at max N.
- Find if a molecule can be formed from 3 atoms using their valence numbers
- Count different numbers possible using all the digits their frequency times
- Count of Numbers in a Range where digit d occurs exactly K times
- Times required by Simple interest for the Principal to become Y times itself
- Find the repeating and the missing number using two equations
- Number formed by the rightmost set bit in N
- Maximum possible time that can be formed from four digits
- Check if a number is formed by Concatenation of 1, 14 or 144 only