The Highest Common Factor (**HCF**) or Greatest Common Divisor (**GCD**) of two integers is the largest integer that can exactly divide both integers (without a remainder).

For example, the HCF of **60** and **72** is **12**.

## Example 1: Find HCF using for Loop

```
// program to find the HCF or GCD of two integers
let hcf;
// take input
let number1 = prompt('Enter a first positive integer: ');
let number2 = prompt('Enter a second positive integer: ');
// looping from 1 to number1 and number2
for (let i = 1; i <= number1 && i <= number2; i++) {
// check if is factor of both integers
if( number1 % i == 0 && number2 % i == 0) {
hcf = i;
}
}
// display the hcf
console.log(`HCF of ${number1} and ${number2} is ${hcf}.`);
```

**Output**

Enter a first integer: 60 Enter a second integer: 72 HCF of 60 and 72 is 12.

In the above program, the user is prompted to enter two positive numbers.

The `for`

loop is used to iterate from **1** to numbers entered by the user.

The `if`

condition and modulus operator `%`

is used to find the HCF of both numbers.

In the above condition, if both the integers `number1` and `number2` are exactly divisible by `i`, the highest integer value that fulfils that condition is calculated.

## Example 2: HCF using while Loop and if...else

```
// program to find the HCF or GCD of two integers
// take input
let number1 = prompt('Enter a first positive integer: ');
let number2 = prompt('Enter a second positive integer: ');
// looping until both numbers are equal
while(number1 != number2){
if(number1 > number2) {
number1 -= number2;
}
else {
number2 -= number1;
}
}
// display the hcf
console.log(`HCF is ${number1}`);
```

**Output**

Enter a first integer: 60 Enter a second integer: 72 HCF is 12

In the above program, a `while`

loop is used with an `if...else`

statement.

In each iteration, the smaller integer is subtracted from the larger integer. And the result is assigned to a variable holding a larger integer.

The `while`

loop continues until both the integers become equal.