Because it doesn't matter what numbers you select to start the tree. If you do it correctly, the bottom branch will always have the same numbers.
factor trees and prime factor trees are the same thing with different names.
No, although if done correctly, their bottom branches will all have the same numbers.
Yes.
common factor
When the lowest number is a factor of the other two.
All numbers with a least common multiple, have that multiple as a factor.
A factor rainbow, like factor trees, ladders, fireworks, lattices and cakes is a way to notate the process of finding the prime factorization of a given number. The process remains the same. If you would like to found a new method, just figure out a different way to write the numbers on the page.
Only if the magnitudes of two numbers are the same.
The smell isn't the same
They have different numbers of neutrons.
There are factor trees, fireworks and rainbows, but these are just different ways of notating the same process. There are also ladders and continuous division.
When the numbers have a common factor (other than 1).