27. Collecting all prime factors of a given number

A prime number is a number divisible by itself and 1 (for instance, 2, 3, and 5 are prime numbers). Having a given number, we can extract its prime factors, as in the following figure:

Figure 1.22: Prime factors of 90 are 2, 3, 3, and 5

The prime factors of 90 are 2, 3, 3, and 5. Based on Figure 1.22, we can create an algorithm to solve this problem, as follows:

1. Define a List to collect prime factors of the given v.
2. Initialize a variable s with 2 (the smallest prime number).
3. If v % s is 0, collect s as a prime factor and compute the new v as v / s.
4. If v % s is not 0, then increase s by 1.
5. Repeat step 3 as long as v is greater than 1.

In code lines, this O(n) algorithm (O(log n) for composite numbers) can be expressed as follows:

public static List<Integer> factors(int v) {
  List<Integer> factorsList = new ArrayList<>();
  int s = 2;
  while (v > 1)...