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

Math Antics - Prime Factorization - By mathantics

Transcript


00:03	Uh huh . Hi , welcome to Math Antics .
00:08	In this video , we're going to learn something called
00:10	Prime Factory Ization , wow . That sounds pretty complicated
00:14	, doesn't it ? But don't worry , it's not
00:16	that bad now . From the name Prime Factor Ization
00:20	, you can probably guess that it involves factoring like
00:22	we learned about in the last video . But what
00:25	about this word ? Prime here ? What does that
00:27	mean ? Well , to help you understand that ,
00:29	let's use what we learned in the last video to
00:32	factor the number seven . Well , let's see .
00:34	We could get seven by adding three and four .
00:37	But factoring is not about what you can add to
00:40	get a number . It's about what you can multiply
00:42	. Well , since I can't think of any numbers
00:44	that would work , let's find factors by testing for
00:47	the visibility . Now , I'm gonna do this really
00:49	fast using my calculator . Let's see . Okay ,
00:56	okay , here's the numbers I got . That's interesting
01:01	. The only two numbers that didn't leave remainders were
01:04	one in seven and those are kind of obvious .
01:06	We know that if you multiply any number by one
01:09	, you'll just get that same number . But why
01:11	aren't there any other factors of seven ? All right
01:15	. Here's why seven is a special kind of number
01:18	called a prime number . Now ? A prime number
01:21	is just a number that has exactly two factors itself
01:24	. And one there's a lot of prime numbers here
01:27	is the list of all the prime numbers that are
01:29	less than 22 357 11 , 13 , 17 and
01:35	19 . They're the ones you use most often .
01:38	Now , some of you might be wondering why one
01:40	isn't on the list of prime numbers ? Well ,
01:42	one is a lot like a prime number , but
01:45	for some technical reasons it's not considered prime . Okay
01:49	, so in a way , prime numbers are just
01:51	special numbers that you can't factor . Well , unless
01:54	you use the obvious factors of one and the number
01:56	itself . But what's so special about prime numbers anyway
01:59	? Why do we need to know about them ?
02:01	Well , prime numbers are like the building blocks of
02:04	the other whole numbers . In fact , whole numbers
02:07	that are not prime are called composite numbers because they
02:10	are composed of primes . That means that you can
02:13	get them by multiplying prime numbers together . Here's a
02:16	good way to see how that works again . Will
02:18	list all the prime numbers that are less than 20
02:20	. And now let's list all the composite numbers that
02:23	are less than 20 over here . The first composite
02:25	number is four and you get four by multiplying the
02:28	primes two times two . The next composite number is
02:31	six and you get it by multiplying the Primes two
02:35	times 3 . And the next composite number is eight
02:38	. Which you get by multiplying the primes two times
02:40	two times two . And the composite number nine can
02:44	be made by multiplying the Primes three times 3 .
02:47	We could keep going like this and you would see
02:49	that all the composite numbers are made by multiplying different
02:52	combinations of prime numbers together . And each of these
02:55	combinations is called the prime factor Ization of its composite
02:59	number . Ah So the prime factor Ization is a
03:03	thing . It's the set of prime numbers that you
03:05	multiply together to get another number . That's true .
03:09	But you can also use the term prime factor Ization
03:12	as an action to describe how we find out what
03:14	prime numbers a composite number is made of and that's
03:17	what we're gonna do next . We're going to use
03:20	prime factor Ization . The action to find the prime
03:23	factor ization . The set of prime factors for the
03:26	number 12 . And that just means it will continue
03:29	to factor 12 until all the factors are prime numbers
03:33	. Now to do this , I'm going to use
03:35	something called a factor tree . A factor tree is
03:38	just a diagram that helps you keep track of multiple
03:40	factory in steps . When you factor a number ,
03:43	you write the two factors below it with lines or
03:46	branches going to them . And then if you factor
03:49	one of the factors , you do the same thing
03:51	again , You'll see how it works as we do
03:53	this example . So let's get started . 12 can
03:57	be factored into two times six . So we're done
04:00	right . Well , not yet because we're doing prime
04:02	factor Ization . We need to keep going until all
04:05	the factors are prime numbers . So let's see if
04:07	they are . Well , we know that two is
04:09	a prime number but is six prime . No ,
04:12	it's not Because six can be factored into two times
04:15	three And both two and 3 are prime numbers .
04:18	So now we're done factory . And if we bring
04:21	down that to that we had from the first factoring
04:23	step , we can see that the prime factor ization
04:25	of 12 is two times two times three . Now
04:29	, I know what some of you are thinking .
04:31	I didn't want to factor 12 into two times six
04:34	. I wanted to factor it into four times three
04:37	. Well , okay then let's try it that way
04:40	. This time we'll start by factoring 12 into four
04:42	times three . But remember , we need to keep
04:45	factoring until all of our factors are prime numbers .
04:48	So let's see our four and three prime numbers .
04:50	Well , three is prime , but four is not
04:52	, four can be factored into the primes two times
04:55	two . And again , if we bring down that
04:57	three from the first step , We see that we
04:59	have three prime factors for 12 And they're the exact
05:02	same ones that we got the first time . That
05:05	means no matter which way you start factoring as long
05:08	as you factor all the way down to prime numbers
05:10	, you'll always end up with the same group of
05:12	prime factors . Let's try just one more to make
05:15	sure you've got it . Let's find the prime factor
05:18	ization of 42 . Well , for the first step
05:21	of our factory , I see that 42 is an
05:23	even number . So that means that we can divide
05:25	it by two to get our first two factors .
05:28	So 42 divided by two equals 21 . So we
05:31	can factor 42 into two times 21 . Okay ,
05:35	two is prime . So we can't factor it anymore
05:37	. But what about 21 ? Well , if you've
05:40	memorized your multiplication table , you might recognize that 21
05:43	is one of the answers on it . You can
05:45	get 21 by multiplying three times seven . So we
05:48	can factor 21 into three times seven . And if
05:51	you didn't remember that , you could have just done
05:53	some day visibility test and you would have figured it
05:55	out . Okay . So what about the three and
05:58	seven ? Well , they're both prime . So that
06:01	means that we're done factory . We bring down the
06:03	two from the first step and we can see that
06:05	the prime factor ization of 42 is two times three
06:09	times seven . All right . Now , you know
06:12	what prime numbers are and you know how to use
06:14	prime factor Ization to find the set of prime factors
06:17	that composite numbers made of . And that set of
06:19	numbers is also called its prime factor Ization . Just
06:23	to confuse you . As usual . It's important to
06:26	practice what you've learned in this video so that you'll
06:28	get good at it and you can practice by doing
06:30	the exercises for this section . Good luck . And
06:33	thanks for watching Math Antics . See you next time
06:36	. Learn more at Math Antics dot com .

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