Expanding numbers

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I'm taking an assessment test tomorrow on Embry Riddle University online and I'm brushing up on my pre algebra. I'm trying to learn something but don't know the key
words to use on google to help me learn this. Here's a link to what I'm trying to learn:
www.mathplanet.com

Finding the greatest common factor (Pre-Algebra, Discover fractions and factors) – Mathplanet

www.mathplanet.com www.mathplanet.com

On this webpage, if you scroll down and watch the video, you'll see how this guy is finding the greatest common factor of two expressions.

The way I did it led me to the answer: 8 times x cubed. The way this guy in the video did it was different but still led to the same answer. He describes it as expanding a number. For example, when he expanded 24, he got "2,2,2,3"....but when I expanded it I got "2,3,4,6,8". When I expanded 56, I got "2,4,7". I then took the common factors and I did the math of 2 times 4 times x to the third power and got 8 times x to the third power. I came up with x to the third power because both expressions had three "x"'s when I expanded them.

1. Is the way I did it wrong?
2. Even if the way I did it was wrong, I want to learn how this guy in the video did it. So what key words do I need to use to google out how to learn to do what he did when he expanded the numbers the way he did?

note: also wanted to add that I know how to simply fractions, but I wonder if my "not knowing how to expand numbers like the guy in the video" is connected to the fact that I am really SLOW at simplifying fractions. If so, do I need to relearn how to simply fractions?
 
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His non-standard term "expand" is what the text calls "factorize". I would say he is writing the number as a product of prime factors. The number will be the product of the prime numbers he lists.

I don't know what you mean when you say, "when I expanded it I got "2,3,4,6,8"; I suspect you are listing divisors (though not all of them), which is not what is needed here; the product of these numbers is not 24. I can't see how you got the right answer using your lists of numbers; it may be an accident.

There are several ways to find the prime factorization of a number; here is a good source: https://www.mathsisfun.com/prime-factorization.html

There are also several ways to find the GCF of expressions; this shows several of them (#2 is the one on your page): https://www.mathsisfun.com/greatest-common-factor.html

Neither of those includes variables, but they are the easy part.
 
I am agreeing with Dr. Peterson, but expressing it differently.

You can take any integer greater then 1 and express it a product of primes. If you do this in terms of increasing primes, you will get a unique sequence. For example,

[MATH]1224 = 2 * 612 = 2 * 2 * 306 = 2 * 2 * 2 * 153 [/MATH] ...............................fixed typo

We have an odd number so there are no more factors of 2.

[MATH]2 * 2 * 2 * 153 = 2 * 2 * 2 * 3 * 51 = 2 * 2 * 2 * 3 * 3 * 17.[/MATH]
17 is prime, so we are done. And, in terms of increasing primes, that factoring is unique.

What you were doing is finding factors rather than prime factors. It is usually best to start by finding the unique prime factorization.
 
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Ok, after going over what you guys have said, I still don't know how to do what he does but I finally found out what it's called. It took me reading the page on this link for the third time to notice it.

I think what I'm trying to figure out how to do is called "fractioning numbers"

www.mathplanet.com

Finding the greatest common factor (Pre-Algebra, Discover fractions and factors) – Mathplanet

www.mathplanet.com www.mathplanet.com

if you go back to that link, and look at the text before the video you'll see a fraction: 2,000/1,500

Right above that fraction you see the words "Fraction all numbers and find all common factors"

When I read the instructions, I must have misread it and though it said "factor all numbers and find all common factors"
it took me a while but I found all the factors between 1 and 1500 and 2 and 2000.

On that webpage, after 'fractioning all numbers', for 1,500(whatever fractioning means), he came up with a list of numbers:
2*2*2*5*5*10

And when the same thing was done for 2,000, they got the list: 2*3*5*5*10

I don't know what fractioning numbers means(as per what this webpage said), so mabye that's why I don't know how to come up with that list.

if fractioning means factoring, I can come up with a list of factors for 1500 or 2000 and even all the factors but it wouldn't be the same list of numbers shown in the web page, so 'fractioning numbers' must mean something else.

So what is it that I don't know how to do, that's keeping me from being able to do this? What's fractioning numbers. I'm googling that out as you are reading this, I'm just dropping this question off here while I'm looking into this.
 
There's no such thing as "fractioning numbers". That's a typo; clearly they mean "factor", just as they did earlier when they said "factoring both numbers" and then "factorize the numbers".

What they do there is to factor both 2000 and 1500. (They didn't fully factorize, to prime factors, apparently because they saw 10 as a common factor and didn't bother taking it further because they happen to know it doesn't matter. It would be nice if they at least tried to explain that.)

We both told you about factoring (prime factorization). Learn to do that. Can you show us what you get for 1500 and for 2000?

And don't use that site any more; they apparently have no desire to be consistent and help readers understand what they are doing. (But you might want to write to them and ask what they mean by fractioning. They should at least apologize and fix it.)
 
JeffM said:
I am agreeing with Dr. Peterson, but expressing it differently.

You can take any integer greater then 1 and express it a product of primes. If you do this in terms of increasing primes, you will get a unique sequence. For example,

[MATH]1224 = 2 * 612 = 2 * 2 = 306 = 2 * 2 * 2 * 153.[/MATH]
Click to expand...
You had me really upset for a moment! I was about to yell "2*612 is NOT equal to 2*2 and 2*2 is NOT equal to 306!"

But it's just a typo. You have "=" where you intended "*":
[MATH]1224 = 2 * 612 = 2 * 2 * 306 = 2 * 2 * 2 * 153.[/MATH]We have an odd number so there are no more factors of 2.

[MATH]2 * 2 * 2 * 153 = 2 * 2 * 2 * 3 * 51 = 2 * 2 * 2 * 3 * 3 * 17.[/MATH]
17 is prime, so we are done. And, in terms of increasing primes, that factoring is unique.

What you were doing is finding factors rather than prime factors. It is usually best to start by finding the unique prime factorization.
Click to expand...
 
2,3,4,6,8: Since 2*3*4*6* is not 24 it is not true that the prime factorization of 24 is 2*3*4*

2,2,2,3: Since 2*2*2*3 = 24 and 2 and 3 are prime numbers it is true that the prime factorization of 24 is 2*2*2*3

2,4,7: While it is true that 2*4*7 = 56, it is not true that 2, 4 and 7 are all prime numbers. 4 is not prime.

2,2,2,7 : Since 2*2*2*7 = 56 and 2 & 7 are prime numbers then the prime factorization of 56 is 2*2*2*7
 
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