Fallacy
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factor tree of 216
The prime factor tree of 280 is:140,270,2,235,2,2,27,5,2,2,2
There are at least nine different factor trees for 2000, one for each of its non-trivial factor pairs. Eighteen, if you consider the reverse of each pair to be a separate pair. The important information to remember is that it doesn't matter what factor pair you choose to start the tree. But since, if done correctly, all the factor trees will have the same number of branches and arrive at the same factors for the bottom branch, it's a waste of time to write them all out. 2000 1000,2 500,2,2 250,2,2,2 125,2,2,2,2 25,5,2,2,2,2 5,5,5,2,2,2,2 2000 50,40 25,2,40 5,5,2,40 5,5,2,20,2 5,5,2,10,2,2 5,5,2,5,2,2,2
Factor Tree of 20: ........20 ......../ \ .......4 5 ....../ \ .....2 2
A tree.