Which is the most correct factor tree?

Question

I have been working through some factoring problems that include factor trees.

Problem - using a factor tree, express 54 as a product of prime factors.

My answer:

54

2*27

2*3*9

2*3*3*3

Textbook answer:

54

6*9

2*3*3*3

Although they are both correct, I am curious why the textbook excluded using the prime factor of 2 throughout the tree. Is there a rule or convention I am not aware of that made my answer different from the textbook?

Answer 1

You can do it in any way you want. Prime factorisation is unique (the fundamental theorem of arithmetic), so as long as you don't use any factorisations that aren't true in your working, you'll always end up with the same prime factorisation.

Answer 2

Both of them is correct. There isn't any rules to factor a number. However, the answer should be correct.

$54 = (2)\times(3)^3$