Greatest Common Factor Trick GCF - By tecmath
Transcript
| 00:0-1 | Good day . Welcome to the Tech Math channel . | |
| 00:01 | What we're gonna be having a look at in today's | |
| 00:03 | video is the fastest way of working at the highest | |
| 00:06 | common factor of two given numbers . Okay . And | |
| 00:10 | when I say this , this is the largest number | |
| 00:12 | that goes into both into two numbers . And I'll | |
| 00:14 | give you this is a really , really fast and | |
| 00:16 | a very accurate way of , Of doing this . | |
| 00:19 | Okay . So I'll give you an example . We're | |
| 00:20 | going to try and find , I'll give you 10 | |
| 00:22 | seconds to find The greatest common factor . The highest | |
| 00:25 | common factor . The biggest number that goes into both | |
| 00:27 | . What about 196 and 84 . So I'll give | |
| 00:34 | you 10 seconds to do this And time's just about | |
| 00:39 | up . Hopefully you have the highest common factor , | |
| 00:42 | the greatest common factor of 28 . And if you | |
| 00:45 | had that excellent work , if not , I'm going | |
| 00:48 | to show you how to work this out . And | |
| 00:50 | you might , even if you got it , you | |
| 00:51 | might want to still have a look at this method | |
| 00:52 | anyway . Okay , so how do we get this | |
| 00:55 | greatest common factor so quickly ? I'll show you how | |
| 00:57 | to do this . So what we do is the | |
| 00:59 | following , we look at our two numbers here are | |
| 01:02 | 196 , and we're basically going to choose which is | |
| 01:08 | the smallest 18 is 84 , and we're gonna divide | |
| 01:10 | it into the largest 196 . So 84 into 196 | |
| 01:15 | It goes two times because 84 times 268 this is | |
| 01:19 | a remainder of 28 . Okay , that's this reminder | |
| 01:24 | that we're going to be worried about for the next | |
| 01:25 | step . We're going to move this remainder call into | |
| 01:27 | the next step . Okay ? So 28 we're moving | |
| 01:30 | on to this next step . The other part we | |
| 01:33 | move to the next step is the smallest of our | |
| 01:36 | numbers were the ones that we divided into another . | |
| 01:38 | In this case it was the original two numbers we | |
| 01:40 | had 196 80 for the smallest is 84 . But | |
| 01:45 | if we were going on to the next another step | |
| 01:46 | and another step we choose the smallest out of say | |
| 01:48 | these two . Okay . So what we do is | |
| 01:51 | we repeat this step , How many times has 28 | |
| 01:54 | going to 84 ? It goes in three times , | |
| 01:57 | it goes in three times and there is no remainder | |
| 01:59 | goes in perfectly . So once there's no remainder here | |
| 02:03 | , we stop this because now we know the greatest | |
| 02:06 | common factor . Okay ? And it's this number that | |
| 02:08 | we divided into . Okay . The smaller are two | |
| 02:10 | numbers here . Okay , so it's 28 . So | |
| 02:13 | did you get that ? So pretty much what we | |
| 02:15 | do for this method as we interviewed , dividing the | |
| 02:17 | smaller number into the larger number of our two numbers | |
| 02:19 | . We start with our two numbers were trying to | |
| 02:21 | find the greatest common factor of and we're gonna be | |
| 02:24 | removing any remainder onto this next stage as well as | |
| 02:28 | the smallest one of them from the previous step . | |
| 02:30 | We're going to continue this till we get no remainder | |
| 02:32 | . Once we get no remainder , the number that | |
| 02:34 | we've divided into the other one . Okay , the | |
| 02:36 | smallest of these two , that is our greatest Common | |
| 02:41 | factor or our highest common factor . Okay , so | |
| 02:44 | what about we have a look at a couple more | |
| 02:46 | examples . What about , I'll give you an example | |
| 02:48 | with you're probably gonna be able to look at straight | |
| 02:50 | away and work out the factors of say we had | |
| 02:52 | 72 and 60 . Now you may look at this | |
| 02:56 | straight away and go , hey , the highest common | |
| 02:58 | factor is that that's great if you can , but | |
| 03:02 | I'm just going to use it to show you this | |
| 03:03 | method . So anyway , We're going to divide 60 | |
| 03:06 | into 72 , 60 goes into 72 1 time . | |
| 03:09 | It goes in one time and it has a remainder | |
| 03:12 | of 12 . Okay , so this remainder , we're | |
| 03:17 | going to put down here And we're going to take | |
| 03:19 | the smallest of these two numbers , and we're going | |
| 03:21 | to use that for our next part . So now | |
| 03:24 | we look at 60 and 12 , how many times | |
| 03:27 | there's 12 ? Go into 60 . 12 goes into | |
| 03:30 | 65 times with no remainder . So 12 is our | |
| 03:37 | highest common factor . Yeah . Did you get that | |
| 03:42 | method ? Okay , what about uh we'll go through | |
| 03:46 | another one , okay , uh what about , I'll | |
| 03:50 | give you , I'll give you go with it one | |
| 03:51 | more together and then I'll give you guys a couple | |
| 03:53 | . So what about 148 and 48 . Okay . | |
| 04:00 | So we're looking at , how many times does 48 | |
| 04:03 | going ? 248 . It goes three times . Okay | |
| 04:06 | . 148 goes in three times and it has a | |
| 04:09 | reminder of four . Okay , so we're going to | |
| 04:13 | move , this remainder here is four here And we're | |
| 04:17 | going to move the 48 year , the smaller of | |
| 04:19 | these two down to here . Now we look at | |
| 04:21 | how many times four goes into 48 . four goes | |
| 04:24 | into 48 . 12 times . Okay . It goes | |
| 04:27 | in 12 times and there is no remainder , So | |
| 04:32 | four is our highest common factor . Yeah . What | |
| 04:38 | about , I'll give you a guy doing this . | |
| 04:40 | Okay , so it's it's the remain as we are | |
| 04:42 | interested in . And this is a very , very | |
| 04:44 | old method . This is the Euclidean method of doing | |
| 04:46 | this . It's fairly old . Okay , um what | |
| 04:49 | about you try this with 130 and 78 then you | |
| 04:53 | might want to pause the video and and and do | |
| 04:56 | this . So Hopefully you've done it . Hopefully you've | |
| 05:00 | given it a go . So we're going to see | |
| 05:01 | how many times 78 goes into 130 . Okay . | |
| 05:06 | Tommy Thompson's going , it goes him once And there | |
| 05:09 | is a reminder of 52 . Okay , so I'm | |
| 05:13 | going to put this 52 here And I'm going to | |
| 05:16 | move the smaller of these two numbers is 78 there | |
| 05:20 | there . Okay , so now I see how many | |
| 05:23 | times 52 goes into 78 . He goes in once | |
| 05:26 | . Yeah , because at once with a reminder of | |
| 05:30 | 26 . Okay , so now I'm going to move | |
| 05:34 | is 26 Down here , move the remainder here , | |
| 05:37 | move the smaller these two numbers , the 52 Down | |
| 05:40 | here as well . Okay , how many times is | |
| 05:42 | 26 go into 52 goes in two times , No | |
| 05:47 | reminder . So the highest common factor is 26 . | |
| 05:54 | What about one last happy example for what are you | |
| 05:58 | guys ? Okay . And look , this does work | |
| 06:00 | for really , really big numbers . It's it's excellent | |
| 06:02 | . It's probably the best method for using with big | |
| 06:04 | numbers . Obviously small numbers , you can use your | |
| 06:07 | multiplication knowledge and that gets you fairly far . But | |
| 06:10 | with bigger numbers , this is a really , really | |
| 06:12 | great method . Okay , so what about we give | |
| 06:15 | you this one ? What about 585 ? A really | |
| 06:18 | big number . Well , it's not really big is | |
| 06:21 | it ? But it's a big number . 585 and | |
| 06:24 | 105 you're gonna look already and go , hey , | |
| 06:25 | five goes into that . But what would be the | |
| 06:28 | highest common factor of these two ? So , We | |
| 06:31 | start out , we'd see how many times 105 goes | |
| 06:34 | into Uh 585 days in . Five times you can | |
| 06:39 | see that . Okay , so five times 105 is | |
| 06:42 | gonna be a 525 , there's a remainder of 60 | |
| 06:48 | . Okay , so I'll put the 60 here and | |
| 06:51 | I moved this 105 Down from here . OK . | |
| 06:54 | Oh good . Yeah . Okay . How many times | |
| 06:57 | there's now 60 go into 100 and five goes in | |
| 06:59 | once . Yeah , because two times we've taken up | |
| 07:01 | to 120 , so it goes in once and it | |
| 07:04 | has a remainder 45 . Okay , So we put | |
| 07:10 | the 45 here , Put the 60 here . Hey | |
| 07:14 | look , you can see we're getting somewhere 45 and | |
| 07:16 | 60 . Okay , numbers are getting smaller . Every | |
| 07:18 | time is 45 going to 60 goes in once , | |
| 07:23 | Then there's 15 reminder . Okay , so put the | |
| 07:26 | 15 here , 45 , I reckon it's just probably | |
| 07:29 | work it out now . What ? It is the | |
| 07:31 | highest common factor , because 15 goes into 45 , | |
| 07:33 | it goes in three times , but it has no | |
| 07:37 | remainder . So the highest common factor , you might | |
| 07:40 | have guessed it . It's 15 . Anyway . Hopefully | |
| 07:45 | you like this method . I'd like to give a | |
| 07:46 | big shout out . A few people will learn me | |
| 07:48 | to this . I made a video and a Factor | |
| 07:51 | Factory Ization and how working at the highest common factor | |
| 07:54 | and a few people said , hey , why don't | |
| 07:55 | you do this method ? Why don't you use this | |
| 07:56 | method ? This method is much better . And I | |
| 07:58 | thought , hey , you're right on that one . | |
| 07:59 | Okay , So , so thank you a lot for | |
| 08:01 | those guys . Nikki , I think it was the | |
| 08:03 | first person who got that . Thanks a lot for | |
| 08:05 | that . Anyway . See you next time . Bye | |
| 00:0-1 | . |
Summarizer
DESCRIPTION:
OVERVIEW:
Greatest Common Factor Trick GCF is a free educational video by tecmath.
This page not only allows students and teachers view Greatest Common Factor Trick GCF videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.
GRADES:
STANDARDS:
