The HCF or GCD of two integers is the largest integer that can exactly divide both numbers (without a remainder).

## Example 1: Find GCD of two numbers using for loop and if statement

```
class Main {
public static void main(String[] args) {
// find GCD between n1 and n2
int n1 = 81, n2 = 153;
// initially set to gcd
int gcd = 1;
for (int i = 1; i <= n1 && i <= n2; ++i) {
// check if i perfectly divides both n1 and n2
if (n1 % i == 0 && n2 % i == 0)
gcd = i;
}
System.out.println("GCD of " + n1 +" and " + n2 + " is " + gcd);
}
}
```

**Output**

GCD of 81 and 153 is 9

Here, two numbers whose GCD are to be found are stored in `n1` and `n2` respectively.

Then, a for loop is executed until `i` is less than both `n1` and `n2`. This way, all numbers between 1 and smallest of the two numbers are iterated to find the GCD.

If both `n1` and `n2` are divisble by `i`, `gcd` is set to the number. This goes on until it finds the largest number (GCD) which divides both `n1` and `n2` without remainder.

We can also solve this problem using a while loop as follows:

## Example 2: Find GCD of two numbers using while loop and if else statement

```
class Main {
public static void main(String[] args) {
// find GCD between n1 and n2
int n1 = 81, n2 = 153;
while(n1 != n2) {
if(n1 > n2) {
n1 -= n2;
}
else {
n2 -= n1;
}
}
System.out.println("GCD: " + n1);
}
}
```

**Output**

GCD: 9

This is a better way to find the GCD. In this method, smaller integer is subtracted from the larger integer, and the result is assigned to the variable holding larger integer. This process is continued until `n1` and `n2` are equal.

The above two programs works as intended only if the user enters positive integers. Here's a little modification of the second example to find the GCD for both positive and negative integers.

## Example 3: GCD for both positive and negative numbers

```
class GCD {
public static void main(String[] args) {
int n1 = 81, n2 = -153;
// Always set to positive
n1 = ( n1 > 0) ? n1 : -n1;
n2 = ( n2 > 0) ? n2 : -n2;
while(n1 != n2) {
if(n1 > n2) {
n1 -= n2;
}
else {
n2 -= n1;
}
}
System.out.println("GCD: " + n1);
}
}
```

**Output**

GCD: 9

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