Question 14277: 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 atif.muhammad(135)   (Show Source):
You can put this solution on YOUR website! There is no specific rule to factorisation.
I personally have always started with the smallest number I can think will divide the number (apart from one).
I would have attempted 120 this way.
120
/ \
2 x 60
/ \
2 x 30
/ \
2 x 15
/ \
3 x 5
As you can see above, I've continually divided 120 by the 2. Therfore, the factorisation of 120 is 2 x 2 x 2 x 3 x 5. Done!
Supposing I divided by 3 first instead.
120
/ \
3 x 40
/ \
2 x 20
/ \
2 x 10
/ \
2 x 5
The factors I get this time are 120= 3 x 2 x 2 x 2 x 5.
As you can see, I doesn't matter which number I factorise out of the original number first. In the end you get the same answer.
Supposing I divided by 4 first as well.
120
/ \
4 x 30
/ \ / \
2 x 2 3 x 10
/ \
2 x 5
The factors I get this time are 120= 2 x 2 x 3 x 2 x 5.
As you can see, if you divide by four, you have to do an extra step as four can been divided by 2 as well.
You should always start with the smallest number you can think of which can completely divide the original number (apart from 1!).
The teacher's method was original correct as she started with 2. You started with 4 which could be divided further as well. As you as you did what I did with the "division by 4" above, you should be fine.
The teacher should accept both of your methods in fact.
36 = 2 x 2 x 3 x 3 is as correct as 36 = 3 x 2 x 3 x 2
Don't worry! Maths is very flexible! 6 = 3 x 2 is the same as 6 = 2 x 3, right?!
Any other problems, feel free to email me at atif.muhammad@gmail.com
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