Math Antics - Factoring - Free Educational videos for Students in K-12

Math Antics - Factoring - By mathantics

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00:03	Uh huh Hi and welcome to Math antics . In
00:08	today's lesson , we're going to learn all about factoring
00:11	. Factoring is a math operation . It's something you
00:14	do to a number now with the other math operations
00:17	you've done so far , you're given two or more
00:19	numbers to work with . But with factoring you only
00:22	get one number . That's because factoring is like being
00:25	given the answer to a multiplication problem and then having
00:28	to figure out what that problem was . So you
00:30	can think of factoring as unm multiplying When you multiply
00:34	, you take two numbers and multiply them together to
00:37	get one number . And when you factor you take
00:39	one number and figure out what two numbers you can
00:42	multiply together to get that number . For example ,
00:45	let's say you're asked to factor the number 10 .
00:48	Now that means that you need to figure out what
00:49	numbers you can multiply together to get 10 . If
00:53	you know your multiplication table , you'll remember that two
00:55	times five equals 10 . That means that two and
00:58	five are factors of 10 . So factors are just
01:01	the parts of a multiplication problem . And factoring is
01:04	figuring out what those parts are . I'm sure some
01:07	of you are wondering why would I ever want to
01:09	factor a number now ? That's a good question and
01:12	I have a good answer . Factoring can make solving
01:15	some math problems easier . For example , factoring is
01:19	really useful for simplifying fractions . By breaking a number
01:22	up into its factors you can sometimes cancel out factors
01:25	that aren't really needed for now though , you just
01:28	need to learn what factoring is and how to do
01:30	it . So let's see another example . Let's factor
01:33	the number 24 for this one . I think I'll
01:35	use my multiplication table . Let's see here . Alright
01:39	, well four times six is 24 . So that
01:41	means that four and six are factors of 24 .
01:44	Now , hold on , I'm sure some of you
01:46	have seen that three times eight is also 24 that's
01:49	true . We could have decided to factor 24 in
01:52	23 times eight instead . So which of the factories
01:54	is right , Is it four and six or three
01:57	and eight ? Actually they're both right . There can
02:00	be more than one way to factor a number .
02:02	That's one of the things that might make factory in
02:04	a little confusing . At first you're used to having
02:06	just one right answer because when you add subtract multiply
02:10	or divide there is just one right answer . But
02:12	when you factor or a new multiply a number ,
02:15	you might find that there's more than one correct way
02:17	you can do it . So we can see that
02:19	the number 24 has quite a few factors for is
02:22	a factor six is a factor three is a factor
02:25	and eight is a factor . The fact that each
02:28	of these numbers is a factor of 24 means that
02:30	each of them can divide evenly into 24 and when
02:33	I say divide evenly , I mean that it will
02:35	divide in without a remainder . For example , if
02:38	we take our first factor four and divide it into
02:41	24 using a calculator , our answer will be 64
02:45	divides into 24 6 times with no remainder . But
02:49	what if we try to divide 24 by a number
02:51	that isn't one of our factors like the number seven
02:54	, If we try 24 divided by seven on a
02:56	calculator , we get 3.42857 , Blah Blah Blah .
03:02	A long decimal number that didn't divide it evenly because
03:05	there's a big remainder . What we just did is
03:08	called testing for the visibility Testing for the visibility is
03:11	a way to find out if a number is a
03:12	factor of another number with the test we just did
03:16	. We confirmed that four is a factor of 24
03:18	, but seven is not . Sometimes you may be
03:21	asked to find all the factors of the number .
03:23	If that happens , you can use testing for the
03:25	visibility to solve the problem , To see how it
03:28	works . Let's try to find all the factors of
03:30	24 . We already know four of them . But
03:33	there's a lot more numbers we can test , fortunately
03:35	, we only need to test numbers that are less
03:37	than half of the number we're testing and since half
03:40	of 24 is 12 , we just need to test
03:42	the numbers one through 12 to keep things organized .
03:46	Let's list the numbers we're going to test and we'll
03:48	circle the factors that we already know 346 and eight
03:52	. We can also cross out the seven since we
03:55	already tested it and found out it wasn't a factor
03:58	. Okay . Now for the numbers we haven't tested
04:00	yet . Let's start with one . Well , of
04:02	course one is a factor because one will divide evenly
04:05	into any whole number . So one is always a
04:08	factor . And since one is a factor then that
04:10	means that 24 is also a factor because one times
04:14	24 equals 24 . It might seem weird that a
04:17	number is always a factor of itself . But it's
04:19	true knowing that helps you get started listening the factors
04:23	because you can always include one and the number itself
04:27	. Now let's move on and test too . If
04:29	we divide 24 x two , we get 12 .
04:32	So yes , two is a factor because it divided
04:35	evenly . You can factor 24 into two times 12
04:39	. That means that we can also circle 12 as
04:41	a factor of 24 . So any time you do
04:44	a visibility test and the number you're checking passes the
04:47	test then the answer you get from dividing will also
04:50	pass the test . It will also be a factor
04:53	That will speed things up because we know we don't
04:55	have to test 12 . Okay , let's move on
04:58	to the next number . We haven't checked . 5
05:01	24 divided by five equals 4.8 . Well that didn't
05:05	divide evenly because our answer is a decimal number .
05:07	That means that five is not a factor of 24
05:11	. Next we'll try 9 , 24 divided by nine
05:14	equals 2.66666 . That's definitely not a factor . Okay
05:19	, how about 10 24 divided by 10 equals 2.4
05:23	, Nope . That's a decimal number . So 10
05:26	is not a factor . It looks like the last
05:28	one we have to try is 1124 , divided by
05:31	11 equals 2.181818 . That's not a factor either .
05:36	All right . Since we've tested all the numbers that
05:39	are less than half of 24 , we found all
05:41	of its possible factors and they are 123468 12 and
05:48	24 . Now I know that might seem like a
05:51	lot of work but fortunately you probably won't have to
05:54	do many of those problems . The important thing is
05:56	just to know what factoring is and how you can
05:59	use testing for the visibility to help you find factors
06:02	. Alright , that wraps up this lesson but since
06:05	actually doing math is the best way to learn it
06:07	. Be sure to try the exercise problems for this
06:09	section . Thanks for watching and I'll see you next
06:12	time learn more at math . Antics dot com .

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