Is it a good idea to use a factor tree to find the prime factorization of any composite number? Why or why not?

Question

For example, if I use a factor tree for 12, I would know a couple of ways to do it, but I'm going to show you one way: 12=3 x 4: 4 is composite, so 4=2 x 2. We can't factor down any further, so I need to use the prime numbers from what I did to create the prime factorization of 12. So, 3 x 2 x 2=12. A regular factor tree uses a composite number to factor down the multiplication of that number and so on if necessary using lines. Anyway, let's cut to the chase. Is this good for any composite number?

Answer 1

It will always work, for any composite number, but it's only possible in practise if you know a (preferably large) divisor of the number.