Greatest Common Factor - Free Educational videos for Students in K-12

Greatest Common Factor - By tecmath

Transcript


00:0-1	today in this video , what we're going to be
00:01	doing is we're going to be using factor trees to
00:03	work at . The lowest common multiple and the highest
00:06	common factor of two numbers . The lowest common multiple
00:09	is the lowest number that these guys will go into
00:12	. And the highest common factor is the highest common
00:14	number that goes into them . So let's have an
00:17	example here . What about we look at The numbers
00:19	are 36 and 84 . So first off , we're
00:24	going to work out the factor trees of these .
00:26	So let's do this . Okay , so The way
00:30	that we do these is as follows , we're looking
00:32	for numbers that go into both of these . So
00:35	36 Six times six is equal to 36 . You
00:38	can also do 12 times three , but you choose
00:40	whichever one we're going to end up with the same
00:42	answer in the end . Now these are both composite
00:45	numbers . So we can take these even further .
00:47	The numbers are going to six and three and two
00:51	And three and 2 . So now what we've hit
00:54	is the stage where all these numbers here are prime
00:57	. We can't take them down any further . So
00:59	let's go across to the 84 here . So 84
01:02	, what number's going to that now look , you
01:04	can see very easily that four goes into it because
01:07	four goes into both eight and four here And it
01:10	goes in 21 times Both of these numbers , a
01:13	composite numbers , we can take them further 21 ,
01:16	the numbers three and seven go into it for the
01:19	numbers to and to go into it . But now
01:22	what we've had is a stage where all these numbers
01:24	also a prime and we can use these to work
01:26	out highest common factor and lowest common multiple . So
01:31	first off , I'm going to work out the highest
01:32	common factor and I'll show you how to do this
01:35	. So the highest common factor . This is the
01:38	highest common number that goes into both of these numbers
01:41	. And the way that we do this is as
01:43	follows . Let's look for where we have overlap here
01:47	. What I mean by this similar numbers . So
01:49	there's a three here and three here , There is
01:52	a two here and two here . The seven is
01:55	not , there's no seven in both , but there
01:57	is a two here in the two year . And
01:59	this is how we can work out the highest common
02:01	factor . We just multiply these numbers , we go
02:03	three times two times two . We don't have to
02:06	do it that many times . Just for just once
02:09	. Okay , so three times two is six times
02:12	two is 12 . So the highest common number that
02:14	goes into both of these numbers is 12 . Okay
02:18	, what about now ? We work out the lowest
02:21	common multiple . Okay , that is the number ,
02:25	the lowest number that both of these numbers go into
02:29	. Okay , so how do we go about doing
02:30	this ? Well , we're going to use these three
02:33	this to this too As part of error . What
02:35	we're going to be doing . So three times two
02:37	times two we're gonna multiply them by what's left after
02:41	we've done this particular stage here . So after we've
02:43	done this here , we have a three and a
02:45	seven left . We're just going to multiply by these
02:48	Times three times 7 . So what do we have
02:51	three times two times two is 12 Times three is
02:55	36 Times seven is going to be 252 . So
03:02	the lowest number that both 84 and 36 going to
03:06	is 252 . It's not too bad . Right .
03:09	What about we do one more example . Okay .
03:13	What about we work out the highest common factor in
03:16	the lowest common multiple of ? Uh what about we
03:19	do 270 and we do 900 . Okay . Big
03:25	numbers , but pretty easy . Right ? So two
03:27	numbers that go into 2 70 you can look at
03:30	and say , okay , we could go say 30
03:32	and nine because 39 27 with the 10 there ,
03:36	you can also do our three and 90 . But
03:39	like I said , the answers will all be the
03:41	same in the end . Okay , So these are
03:43	both composite numbers here , 10 and three . This
03:46	can break up into this year's the dead end .
03:49	This is a prime number , but 10 can be
03:50	broken up into five and two knowing here three and
03:56	3 . And so we've hit this stage . These
03:58	are all prime . Now , let's do the same
04:00	for 900 . We have 30 x 30 . These
04:04	can be broken up into 10 and three , 10
04:08	and three , and the 10 can be broken down
04:10	further because it's a composite number and they can go
04:13	into five and two . It has the factors of
04:16	five and two . So Alright , awesome . We
04:19	can go through now and work out our our highest
04:22	common factor and our lowest common multiple . So our
04:26	highest common factor . Remember what we did for this
04:29	? We're going to look for numbers that are in
04:30	common here . So five and five . We have
04:34	a two and a two . We have a three
04:37	here and three here , we have a three and
04:39	a three that's left . So we have this three
04:41	over here . Okay , so we're going to go
04:43	five times two times three times three . Five times
04:49	two is 10 times three is 30 times three .
04:53	We have the answer of 90 . What about the
04:56	last little part here where we're going to work out
04:58	the lowest common multiple ? So we're gonna get this
05:01	90 here . We know it's going to be the
05:03	same and we're just gonna multiply by what's left times
05:06	three times five times two times three times five times
05:11	two , 90 times three is 270 Times five times
05:17	2 , five times 2 is 10 . So 270
05:19	times 10 is 2700 . And so that's the smallest
05:25	number that both of these are lowest number that both
05:28	of these numbers going to . So it's not too
05:30	bad . Right ? It's pretty easy anyway . We'll
05:33	see you next time . Bye .

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