Prime Factorization - Free Educational videos for Students in K-12

Prime Factorization - By Anywhere Math

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00:0-1	I have 24 deaths in my classroom . And at
00:02	the beginning of every year , I try to figure
00:05	out how I want to group them . If every
00:07	group needs the same number of deaths , how many
00:10	different arrangements can I make ? Welcome to anywhere .
00:31	Math . I'm Jeff , Jacobson . And today we're
00:33	gonna talk about prime factor ization . Okay . How
00:38	am I going to arrange those deaths ? So remember
00:42	I've got 24 total . Okay . And there's a
00:47	lot of different options . I have . Uh ,
00:50	first I could put everybody together in one big group
00:53	. Right ? I could have one group of 24
00:59	. I probably wouldn't do that . But I could
01:01	, if I wanted , uh , I could split
01:03	them in half . I could do to groups of
01:09	12 each . I could do Three groups of eight
01:18	. So eight per group . That's not terrible .
01:22	It's still pretty big . I can also do four
01:25	groups of six . four times 6 is 24 .
01:33	Um , what I just listen here are called factor
01:36	parents . Uh , if you notice each one of
01:39	these numbers are a factor of 24 , right ?
01:43	24 is divisible by 123468 12 , and 24 .
01:48	They're all factors and we listed them in paris .
01:52	So if you were going to find , if you
01:54	see a problem that's asking about factor pairs , that's
01:57	what you do . You list them in paris and
02:00	it's good to go in order . Always start with
02:02	one . One is always a factor of every number
02:05	. So start with one and then go in that
02:08	order , notice I did one and then 234 And
02:11	then I got to six . You can stop when
02:13	it starts to repeat . But for us for this
02:16	problem I have some other options . I could do
02:20	four groups of six , but then I can also
02:23	do the opposite of that . I can also do
02:25	mhm . six groups of four . Yeah . Instead
02:33	of three groups of eight , I could do eight
02:35	groups of only three deaths . Eight groups of three
02:42	same thing here . Instead of just two big groups
02:46	of 12 deaths , I could do 12 groups of
02:49	only two people , basically Putting them in Paris ,
02:52	12 groups of two , which are just people in
03:00	Paris . Um And then finally , Instead of one
03:04	big group of 24 , I could do 24 groups
03:08	of just one person . So basically everyone is by
03:11	themselves . So there really aren't any groups 24 groups
03:14	of one . Okay , so that's everybody by themselves
03:21	. So the question was , how many different arrangements
03:24	can I make ? Uh well 12345678 So the answer
03:31	I can make eight arrangements . That's for that .
03:37	Right , Okay . Let's try an example with factor
03:40	pairs . So example , one list the factor pairs
03:42	of 56 Factor pairs . All you're looking for are
03:46	factors and we're writing them in pairs . Uh remember
03:49	factors you can think of , well what numbers is
03:52	56 divisible by ? Uh what number goes into 56
03:56	evenly ? That's those are your factors . And like
03:59	I said before , always start with one , One
04:02	is always going to be a factor and we're lifting
04:04	them as pairs . So one times what is 56
04:08	? Well one times 56 Is . 56 . is
04:12	also a factor , right ? Uh and then just
04:15	go in order . It's an even number so too
04:18	is gonna work too , is a factor Uh two
04:21	and 28 . three is not if you know you're
04:26	the visibility rules , The sum of the digits is
04:29	11 . That's not divisible by three , so three
04:32	doesn't work . How about Four , wow , four
04:36	is a factor of 56 . 456 , it goes
04:41	14 times four times 14 is 56 . Uh five
04:47	doesn't work because this last digit doesn't end in a
04:50	five or a zero . Uh six doesn't work because
04:54	we needed a three as a factor Uh if six
04:58	was gonna work Uh seven , hopefully , you know
05:01	, seven times 8 is 56 . So seven and
05:05	8 is another factor pair . Uh and then we're
05:09	done . Once you get to a number that you've
05:11	already got nine , know nothing else . Right ?
05:14	So these are our factor pairs . Now try some
05:17	on your own . All right , let's look at
05:24	example two . It says right , the prime factor
05:27	ization of 48 . Well , first , let's talk
05:30	about what that means . Prime factor Ization . Prime
05:34	factor Ization of a number is just when you write
05:37	a number written . Mhm . As the troops As
05:47	the product of its prime factors . Okay , privatization
06:02	of a number is just a number written as the
06:04	product of its prime factors . You can look if
06:07	you remember prime prime numbers are those that are only
06:10	divisible by one in itself . Uh and factories ation
06:14	your listing the factors , the prime factors . So
06:17	that if you just remember that , look at the
06:19	word , you can hopefully remember what you need to
06:22	do . So basically what we need to do is
06:26	list of factors until we get all prime numbers .
06:29	That's basically what we do . So let's try it
06:32	. And again , if you think you know how
06:33	to do it on your own , go for it
06:35	. Uh So first when you're starting out a good
06:40	way to do it is use a factor tree .
06:42	Uh basically we just start writing factors and it looks
06:45	kind of like a tree . Um there's lots of
06:49	ways we can start uh we can start with two
06:52	and 24 we can start with six and eight .
06:56	Uh We could do four and 12 . It doesn't
07:00	really matter how you start , it's up to you
07:03	if you have an even number , a lot of
07:05	people like to start with to , you know ,
07:07	to is a factor . Okay ? And two times
07:14	uh 24 . Okay , So there's our factor pair
07:19	just like what we did before two times 24 .
07:21	Well two is a prime number , so that's done
07:27	. We're not going to factor that anymore , you
07:30	really can unless you just do two in one ,
07:32	but that's not going to help anything . So we're
07:35	done with that . So now 24 isn't prime ,
07:38	it's composite , it still has other factors besides one
07:42	in itself , so we're going to keep going um
07:45	and it's even so I can do to again two
07:48	times 12 , Two and 12 are both factors of
07:52	24 and again two is prime . So we're done
07:57	with that . I'm going to circle it . Remember
08:00	we're just trying to find all the factors until we
08:03	get to all prime factors . 12 is not prime
08:07	. It's composite . So we're going to keep going
08:09	. It's even so I can do to again two
08:12	times six . No , there's another two that's prime
08:17	. So it's done . Six is still composite .
08:20	So we're not done with that . So finally running
08:24	out of room a little bit too , times three
08:29	is six . Those are two factors of six and
08:33	two and 3 are both prime numbers . So I'm
08:36	going to circle that . And now , once there's
08:41	no more composite numbers , You're done . So my
08:45	prime factor ization of 48 is two times two times
08:53	22 times two times two . You're just following all
08:55	the ones that you circled times two Times three .
09:01	That's the prime factor Ization Of 48 . Remember ?
09:05	It's the product of all its prime factors . Product
09:08	meaning multiplication . Right ? Those are all the prime
09:12	factors . Now , we can shorten this . Hopefully
09:16	you remember if we've got repeated multiplication instead of two
09:20	times two times two times two , we can use
09:22	exponents if you remember a couple of videos ago ,
09:25	so we can write that as 2 to the 4th
09:28	. Yeah , Times three . It's a little simpler
09:31	. Either one is correct . This one is maybe
09:35	just a little easier to read . So that is
09:37	the prime factor ization of 48 . Here's some to
09:40	try on your own . Thanks for watching . And
09:48	if you like this video , please subscribe .

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