## GCD of three numbers

### C

Definition of HCF (Highest common factor):

HFC is also called greatest common divisor (gcd). HCF of two numbers is a largest positive numbers which can divide both numbers without any remainder. For example HCF of two numbers 4 and 8 is 2 since 2 is the largest positive number which can dived 4 as well as 8 without a remainder.

Logic for writing program:

It is clear that any number is not divisible by greater than number itself.

☆In case of more than one numbers, a possible maximum number which can divide all of the numbers must be minimum of all of that numbers.

For example: 10, 20, and 30
Min (10, 20, 30) =10 can divide all there numbers. So we will take one for loop which will start form min of the numbers and will stop the loop when it became one, since all numbers are divisible by one. Inside for loop we will write one if conditions which will check divisibility of both the numbers.

Program :

`#include<stdio.h>int gcd(int , int , int);int main(){int i , j , k , g;scanf("%d %d %d", &i , &j , &k);g = gcd(i , j , k);printf("%d",g);return 0;}int gcd(int i , int j , int k){int least;least = i;while(!( (i == j) && (j == k) ) ){i = (i == 0 ? least : i);j = (j == 0 ? least : j);k = (k == 0 ? least : k);if(i <= j){if(i <= k)least = i;elseleast = k;}else{if(j <= k)least = j;elseleast = k;}i = i % least;j = j % least;k = k % least;}return least;}`

### Java

```import java.util.*;

public class HCFOFNumbers {
public static int hcf(int a, int b) {
if (b == 0)
return a;
else
return hcf(b, a % b);
}

public static int hcf(int a, int b, int c) {

return hcf(hcf(a, b), c);

}

public static void main(String[] args) {
Scanner input = new Scanner(System.in);
System.out.print("Enter Number 1: ");
int num1 = input.nextInt();
System.out.print("Enter Number 2: ");
int num2 = input.nextInt();
System.out.print("Enter Number 3: ");
int num3 = input.nextInt();
int hcfOfNumbers = HCFOFNumbers.hcf(num1, num2, num3);
System.out.println("HCF of three numbers " + num1 + "," + num2
+ " and " + num3 + " is: " + hcfOfNumbers);
}
}```