SOLUTION: This is the way the teacher wrote down the factorization of 36. (But shouldn't the factorization in the diagram be in the correct factor order of 2x2x3x3 and NOT 3x2x3x2 ?) Wh

Question 14276: This is the way the teacher wrote down the factorization of 36. (But shouldn't the factorization in the diagram be in the correct factor order of 2x2x3x3 and NOT 3x2x3x2 ?)
Why not:
....MY WAY....................TEACHER'S WAY
......36................................36..........
....../\................................./\.........
...4..X..9..........................6..X..6.........
..../\..../\.........................../\..../\.....
..2x2..X.3x3.......................3x2..X..3x2......
..2X2X3X3...........................2X2X3X3.........
Wouldn't this MY way be correct also?
My son and I are having a problem with diagramming a prime factorization 'tree' (tree is the name given for the drawing). When I diagram a whole number to get its factors, how can I tell what number I should start our with first in the diagram? e.g. MY WAY started with '4'. When I (mom) asked the teacher to send home how to do the tree, her tree started with '2' FIRST (see below). How do I figure out what number the tree diagram should start with underneath the whole number? Is there a specific rule to follow?

Whole number 120 was a problem my son had for homework last night (10/06/05-Thurs). He has a test on this subject Tuesday, 10/11/05 and he still doesn't understand how to do the tree, nor do I know how to help him.

According to a prime factorization chart 120 = 2x2x2x3x5.) Since its very hard to memorize such a listing, how do I know to start my diagram with the number '2'? Why not start with numbers: 120, then underneath, 6 x 20? Then under the 20 would go.... I know know??
PLEASE HELP---A mom who has been out of school since 1974!
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
to be honest i would disagree with both your methods :-) However, neither method is wrong i think.

Remember, you are looking for primes: 2,3,5,7,11,... etc So, use those.

I would do the following:
36
2x18
2x2x9
2x2x3x3

Can you see what i did?...i start with the number and ask myself is it divisible by 2?. I write those factors down.

I then look at the 18...is it divisble by 2? If so, write it down --> 2x9. Etc etc just build it up that way.

eg 120
2x60
2x2x30
2x2x2x15
2x2x2x3x5

see?

jon.