One.
prime number
A power.
I would call an odd number factor a factor that is an odd number. I would call a number with an odd number of factors a perfect square.
I call it odd.
I call it 1.
17, being a prime number, has one prime factor, itself. Whether you call that one branch or no branches, it won't be a tree.
A Factor
when it goes into another number
It is called a common factor!
It is a factor of the number to be divided
It is not possible to give a sensible answer to this question. The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question so, mathematically, the question does not make sense. If, instead, you consider a number [positive integer] whose greatest common factor is one, then there is only one possibility and that is the number one. So you would call it ONE.
Every composite number has its own unique tree, so I guess the answer is all numbers have one tree. Perhaps you meant one branch or one factor. Prime numbers only have two factors, one of them is prime, so if you try to do a factor tree with a prime number, it stops the second you write the number down. And then there's one. One only has one factor, so we won't even bother with a tree. We'll call it a factor twig.