calculateGCDArray()

Step 1: Understand the Problem

We want to write a function in JavaScript to calculate the Greatest Common Divisor (GCD) of all numbers in an array. The GCD of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder. For example, the GCD of 8 and 12 is 4, because 4 divides both 8 and 12 exactly.

To do so, we will start with a helper function that calculates the GCD of two numbers, and then expand this to handle an array of numbers.

javascript
function gcd_two_numbers(x, y) {
  while(y) {
    var t = y;
    y = x % y;
    x = t;
  }
  return x;
}

Step 2: Recursive Approach

In this helper function, we are using the Euclidean algorithm to compute the GCD of two numbers. We can apply this helper function recursively to an array of numbers. We will write a recursive function that calls itself until the array length is 1 (which means we have found the GCD of all numbers).

Step 3: Implement the Recursive Function

In this step, we will implement the recursive function as described above. This function will use our helper function gcd_two_numbers to compute the GCD of the first two numbers, then replace the first two numbers with their GCD, and call itself with the new array.

javascript
function gcd_array(numArray) {
  if(numArray.length === 2) {
    return gcd_two_numbers(numArray[0], numArray[1]);
  } else {
    return gcd_array([gcd_two_numbers(numArray[0], numArray[1])].concat(numArray.slice(2)));
  }
}

Step 4: Test Function

Now that we have implemented our gcd_array function, we need to test it to make sure it works correctly.

javascript
gcd_array([12, 18, 30]);  // should return 6

Conclusion

In this blog post, we have written a JavaScript function to calculate the GCD of an array of numbers. We started with a helper function that computes the GCD of two numbers using the Euclidean algorithm, and then expanded this to handle an array of numbers using a recursive approach.

javascript
function gcd_two_numbers(x, y) {
  while(y) {
    var t = y;
    y = x % y;
    x = t;
  }
  return x;
}

function gcd_array(numArray) {
  if(numArray.length === 2) {
    return gcd_two_numbers(numArray[0], numArray[1]);
  } else {
    return gcd_array([gcd_two_numbers(numArray[0], numArray[1])].concat(numArray.slice(2)));
  }
}

This function works for any array of positive integers, and computes the GCD in O(n log n) time, where n is the length of the array.