HCF (Highest Common Factor) or GCD (Greatest Common Divisor) of two numbers is the largest number that divides both of them.

For example GCD of 20 and 28 is 4 and GCD of 98 and 56 is 14.

A **simple solution** is to find all prime factors of both numbers, then find intersection of all factors present in both numbers. Finally return product of elements in the intersection.

An **efficient solution **is to use Euclidean algorithm which is the main algorithm used for this purpose. The idea is, GCD of two numbers doesn’t change if smaller number is subtracted from a bigger number.

## C

`// C program to find GCD of two numbers` `#include <stdio.h>` `// Recursive function to return gcd of a and b` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `// Everything divides 0` ` ` `if` `(a == 0 && b == 0)` ` ` `return` `0;` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` `// base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a - b, b);` ` ` `return` `gcd(a, b - a);` `}` `// Driver program to test above function` `int` `main()` `{` ` ` `int` `a = 0, b = 56;` ` ` `printf` `(` `"GCD of %d and %d is %d "` `, a, b, gcd(a, b));` ` ` `return` `0;` `}` |

## Java

`// Java program to find GCD of two numbers` `class` `Test {` ` ` `// Recursive function to return gcd of a and b` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `// Everything divides 0` ` ` `if` `(a == ` `0` `&& b == ` `0` `)` ` ` `return` `0` `;` ` ` `if` `(a == ` `0` `)` ` ` `return` `b;` ` ` `if` `(b == ` `0` `)` ` ` `return` `a;` ` ` `// base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a - b, b);` ` ` `return` `gcd(a, b - a);` ` ` `}` ` ` `// Driver method` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `a = ` `98` `, b = ` `56` `;` ` ` `System.out.println(` `"GCD of "` `+ a + ` `" and "` `+ b` ` ` `+ ` `" is "` `+ gcd(a, b));` ` ` `}` `}` |

## Python3

`# Recursive function to return gcd of a and b` `def` `gcd(a, b):` ` ` `# Everything divides 0` ` ` `if` `(a ` `=` `=` `0` `and` `b ` `=` `=` `0` `):` ` ` `return` `0` ` ` ` ` `if` `(a ` `=` `=` `0` `):` ` ` `return` `b` ` ` ` ` `if` `(b ` `=` `=` `0` `):` ` ` `return` `a` ` ` ` ` `# base case` ` ` `if` `(a ` `=` `=` `b):` ` ` `return` `a` ` ` `# a is greater` ` ` `if` `(a > b):` ` ` `return` `gcd(a` `-` `b, b)` ` ` `return` `gcd(a, b` `-` `a)` `# Driver program to test above function` `a ` `=` `98` `b ` `=` `56` `if` `(gcd(a, b)):` ` ` `print` `(` `'GCD of'` `, a, ` `'and'` `, b, ` `'is'` `, gcd(a, b))` `else` `:` ` ` `print` `(` `'not found'` `)` `# This code is contributed by Danish Raza` |

## C#

`// C# program to find GCD of two` `// numbers` `using` `System;` `class` `GFG {` ` ` `// Recursive function to return` ` ` `// gcd of a and b` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `// Everything divides 0` ` ` `if` `(a == 0 && b == 0)` ` ` `return` `0;` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` `// base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a - b, b);` ` ` `return` `gcd(a, b - a);` ` ` `}` ` ` `// Driver method` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `a = 98, b = 56;` ` ` `Console.WriteLine(` `"GCD of "` `+ a + ` `" and "` `+ b` ` ` `+ ` `" is "` `+ gcd(a, b));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP program to find GCD` `// of two numbers` `// Recursive function to` `// return gcd of a and b` `function` `gcd(` `$a` `, ` `$b` `)` `{` ` ` `// Everything divides 0` ` ` `if` `(` `$a` `==0 && ` `$b` `==0)` ` ` `return` `0 ;` ` ` ` ` `if` `(` `$a` `== 0)` ` ` `return` `$b` `;` ` ` ` ` `if` `(` `$b` `== 0)` ` ` `return` `$a` `;` ` ` `// base case` ` ` `if` `(` `$a` `== ` `$b` `)` ` ` `return` `$a` `;` ` ` ` ` `// a is greater` ` ` `if` `(` `$a` `> ` `$b` `)` ` ` `return` `gcd( ` `$a` `-` `$b` `, ` `$b` `) ;` ` ` `return` `gcd( ` `$a` `, ` `$b` `-` `$a` `) ;` `}` `// Driver code` `$a` `= 98 ;` `$b` `= 56 ;` `echo` `"GCD of $a and $b is "` `, gcd(` `$a` `, ` `$b` `) ;` `// This code is contributed by Anivesh Tiwari` `?>` |

## Javascript

`<script>` `// Javascript program to find GCD of two numbers` `// Recursive function to return gcd of a and b` `function` `gcd(a, b)` `{` ` ` ` ` `// Everything divides 0` ` ` `if` `(a == 0 && b == 0)` ` ` `return` `0;` ` ` `if` `(a == 0)` ` ` `return` `b;` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` `// Base case` ` ` `if` `(a == b)` ` ` `return` `a;` ` ` `// a is greater` ` ` `if` `(a > b)` ` ` `return` `gcd(a - b, b);` ` ` ` ` `return` `gcd(a, b - a);` `}` `// Driver code` `var` `a = 98, b = 56;` `document.write(` `"GCD of "` `+ a + ` `" and "` `+` ` ` `b + ` `" is "` `+ gcd(a, b));` ` ` `// This code is contributed by noob2000` `</script>` |

**Output: **

GCD of 98 and 56 is 14

A **more efficient solution **is to use modulo operator in Euclidean algorithm .

## C

`// C program to find GCD of two numbers` `#include <stdio.h>` `// Recursive function to return gcd of a and b` `int` `gcd(` `int` `a, ` `int` `b)` `{` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` `return` `gcd(b, a % b);` `}` `// Driver program to test above function` `int` `main()` `{` ` ` `int` `a = 98, b = 56;` ` ` `printf` `(` `"GCD of %d and %d is %d "` `, a, b, gcd(a, b));` ` ` `return` `0;` `}` |

## Java

`// Java program to find GCD of two numbers` `class` `Test` `{` ` ` `// Recursive function to return gcd of a and b` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{` ` ` `if` `(b == ` `0` `)` ` ` `return` `a;` ` ` `return` `gcd(b, a % b);` ` ` `}` ` ` ` ` `// Driver method` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `a = ` `98` `, b = ` `56` `;` ` ` `System.out.println(` `"GCD of "` `+ a +` `" and "` `+ b +` ` ` `" is "` `+ gcd(a, b));` ` ` `}` `}` |

## Python3

`# Recursive function to return gcd of a and b` `def` `gcd(a,b):` ` ` ` ` `# Everything divides 0` ` ` `if` `(b ` `=` `=` `0` `):` ` ` `return` `a` ` ` `return` `gcd(b, a` `%` `b)` `# Driver program to test above function` `a ` `=` `98` `b ` `=` `56` `if` `(gcd(a, b)):` ` ` `print` `(` `'GCD of'` `, a, ` `'and'` `, b, ` `'is'` `, gcd(a, b))` `else` `:` ` ` `print` `(` `'not found'` `)` `# This code is contributed by Danish Raza` |

## C#

`// C# program to find GCD of two` `// numbers` `using` `System;` `class` `GFG {` ` ` ` ` `// Recursive function to return` ` ` `// gcd of a and b` ` ` `static` `int` `gcd(` `int` `a, ` `int` `b)` ` ` `{ ` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` `return` `gcd(b, a % b);` ` ` `}` ` ` ` ` `// Driver method` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `a = 98, b = 56;` ` ` `Console.WriteLine(` `"GCD of "` ` ` `+ a +` `" and "` `+ b + ` `" is "` ` ` `+ gcd(a, b));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP program to find GCD` `// of two numbers` `// Recursive function to` `// return gcd of a and b` `function` `gcd(` `$a` `, ` `$b` `)` `{` ` ` `// Everything divides 0` ` ` `if` `(` `$b` `==0)` ` ` `return` `$a` `;` ` ` `return` `gcd( ` `$b` `, ` `$a` `% ` `$b` `) ;` `}` `// Driver code` `$a` `= 98 ;` `$b` `= 56 ;` `echo` `"GCD of $a and $b is "` `, gcd(` `$a` `, ` `$b` `) ;` `// This code is contributed by Anivesh Tiwari` `?>` |

## Javascript

`<script>` `// Javascript program to find GCD of two numbers` `// Recursive function to return gcd of a and b` `function` `gcd(a, b)` `{` ` ` `if` `(b == 0)` ` ` `return` `a;` ` ` ` ` `return` `gcd(b, a % b);` `}` ` ` `// Driver code` `var` `a = 98, b = 56;` `document.write(` `"GCD of "` `+ a +` `" and "` `+ b +` ` ` `" is "` `+ gcd(a, b));` `// This code is contributed by Ankita saini` ` ` `</script>` |

**Output: **

GCD of 98 and 56 is 14

Please refer GCD of more than two (or array) numbers to find HCF of more than two numbers.

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