Greatest Common Factor - By Anywhere Math
Transcript
| 00:0-1 | L O L A K A A S A P | |
| 00:03 | T T Y L O M G YOLO and last | |
| 00:09 | but not least . G C F . Yeah , | |
| 00:30 | Welcome to anywhere . Math . I'm Jeff , Jacobson | |
| 00:32 | . And today we're going to add another acronym to | |
| 00:35 | the list . G c F or greatest common factor | |
| 00:40 | . All right . Today is all about the greatest | |
| 00:42 | common factor or more commonly known as the g c | |
| 00:45 | F . So first , let's talk about what is | |
| 00:48 | the greatest common factor . And it's pretty simple if | |
| 00:50 | you just look at the name . Uh the greatest | |
| 00:53 | common factor is just the greatest of the common factors | |
| 00:57 | between two or more numbers . That's all it is | |
| 01:00 | . You find the common factors and then whichever one | |
| 01:03 | is the greatest . That's your G C F . | |
| 01:05 | Let's try an example . There's a couple of ways | |
| 01:08 | we can find the G c F . The first | |
| 01:11 | one we're going to go over is by listing factors | |
| 01:14 | . So I'm going to find the GCF of 24 | |
| 01:16 | and 41st . I'm going to list the factors of | |
| 01:19 | each of those numbers . So 24 I'm gonna go | |
| 01:22 | through my factor pair . So first I always start | |
| 01:25 | with one and 24 . It's an even number . | |
| 01:29 | So I know to works two times 12 is 24 | |
| 01:34 | . I know three works three times eight is 24 | |
| 01:37 | . Also four times six . No five and then | |
| 01:41 | I'm back to six . So those are manufacturers for | |
| 01:43 | 24 . I'm gonna rewrite them in order down here | |
| 01:47 | . So for 20 for my factors are 123 four | |
| 01:55 | six 8 12 and 24 . Okay next I'm going | |
| 02:03 | to list my factors of 40 . I'll do it | |
| 02:06 | in blue . Let's see . So the same thing | |
| 02:09 | For 40 always start with 1 1 and 40 . | |
| 02:13 | Uh it's also even so too is gonna work two | |
| 02:16 | times 20 three is not a factor of 40 so | |
| 02:20 | I skipped that . Four is four times 10 . | |
| 02:25 | Five is because it ends in a zero . So | |
| 02:27 | I know five works five times eight is 46 . | |
| 02:32 | No seven . No we're back to eight so we're | |
| 02:35 | done there . I'm going to do the same thing | |
| 02:38 | and list my factors down here . So 40 in | |
| 02:43 | order one 245 8 10 20 and 40 . Those | |
| 02:54 | are my factors for 40 . Oh now I've got | |
| 02:58 | my factors . Now as the name says G . | |
| 03:02 | C . F . Greatest common factor common means it's | |
| 03:06 | the same in both numbers . It's a factor for | |
| 03:09 | both 24 40 . So what I'm gonna do right | |
| 03:13 | now is I'm gonna circle my common factors . Well | |
| 03:16 | one Is common there in both staying with two same | |
| 03:22 | with four three no five no six no eight yes | |
| 03:28 | 10 no 12 no 2024 40 . So those are | |
| 03:32 | all my common factors 124 and eight . And then | |
| 03:37 | all you gotta ask is , well , which one | |
| 03:40 | is the greatest of the common factors and obviously eight | |
| 03:44 | is the greatest . Some of my final answer . | |
| 03:48 | The greatest common factor of 24 and 40 is hey | |
| 03:55 | GCS Yeah , equals a Okay , let's find the | |
| 04:02 | G c F . Using another strategy for example , | |
| 04:06 | to we're going to find the G C F by | |
| 04:08 | prime factor Ization . So we're gonna do the same | |
| 04:12 | exact problem and just solve in a different way . | |
| 04:14 | Find the GCF of 24 and 40 . We're gonna | |
| 04:17 | use prime factor Ization . So first I'm going to | |
| 04:19 | use a factor tree and figure out what the prime | |
| 04:22 | factor Ization is . Both numbers . If you want | |
| 04:24 | to posit and try to do it on your own | |
| 04:26 | , go for it . So for 24 I've got | |
| 04:30 | lots of options of where to start . It's always | |
| 04:33 | easy to start with two when you have even numbers | |
| 04:35 | . So I'm gonna do that two times 12 . | |
| 04:38 | That's prime . So I'm done with that . Uh | |
| 04:41 | two times 6 . Done two times three . Done | |
| 04:48 | and done . So my prime factor ization of 24 | |
| 04:53 | is gonna be two times two times two times three | |
| 05:00 | . I'm gonna leave it expanded like this instead of | |
| 05:03 | writing two cubes . Uh and you'll see why in | |
| 05:05 | a second . Next let's do prime factor Ization of | |
| 05:08 | 40 48 . I'm gonna start with two again . | |
| 05:14 | Two times 20 is 40 , that's prime . Yeah | |
| 05:19 | Two times 10 is 20 , there's a prime and | |
| 05:24 | then finally two times five is 10 and those are | |
| 05:28 | both prime . So my prime factor Ization of 40 | |
| 05:33 | is two times two times 22 times two times two | |
| 05:39 | times five . So I have my prime factor ization | |
| 05:45 | of 24 and 40 . Done Now , all I | |
| 05:50 | need to look at is see what prime numbers are | |
| 05:54 | in common for both of the prime factors nations . | |
| 05:56 | So you can see They both have a two , | |
| 05:59 | they both have another two and then they both have | |
| 06:02 | a third to so all we have to do to | |
| 06:05 | find the G C f now is multiply . So | |
| 06:10 | they've got 123 twos in common . So two times | |
| 06:14 | two is four times two is eight . So again | |
| 06:17 | , The GC . F of 24 and 40 is | |
| 06:22 | eight . Okay , here's something to try on your | |
| 06:27 | own . Thanks for watching this video . And if | |
| 06:34 | you liked it , please subscribe . |
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