# Program to find HCF (Highest Common Factor) of 2 Numbers

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; ` ` ` ` ` `// 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 = 98, b = 56; ` ` ` `printf` `(` `"GCD of %d and %d is %d "` `, a, b, gcd(a, b)); ` ` ` `return` `0; ` `} ` |

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## 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` `; ` ` ` ` ` `// 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)); ` ` ` `} ` `} ` |

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## Python3

`# Recursive function to return gcd of a and b ` `def` `gcd(a,b): ` ` ` ` ` `# Everything divides 0 ` ` ` `if` `(a ` `=` `=` `0` `or` `b ` `=` `=` `0` `): ` ` ` `False` ` ` `# 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 ` |

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## 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; ` ` ` ` ` `// 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. ` |

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## 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 ; ` ` ` ` ` `// 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 ` `?> ` |

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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; ` `} ` |

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## 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)); ` ` ` `} ` `} ` |

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## 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 ` |

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## 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. ` |

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## 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 ` `?> ` |

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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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