Prime Factorization - By tecmath
Transcript
| 00:0-1 | Hello . This video is part of a series looking | |
| 00:02 | at industries and crimes in this particular lesson . What | |
| 00:04 | we're going to be having to look at is factor | |
| 00:06 | trees . And moreover , how factor trees can be | |
| 00:09 | used to work out the prime factors of any composite | |
| 00:12 | number . So lets us get into this with an | |
| 00:14 | example to say you are asked to work out the | |
| 00:17 | prime factors of 50 by drawing a factor tree . | |
| 00:20 | So we'll start off with 50 here and a factor | |
| 00:23 | tree is where we have these branches coming down . | |
| 00:26 | Uh so what Numbers do we have to go into | |
| 00:30 | 50 and you straightaway say , Okay , we have | |
| 00:31 | five And 10 . These are both factors of 50 | |
| 00:35 | that you can easily see . So If this branches | |
| 00:39 | prime , no other factors would go into these particular | |
| 00:42 | numbers here . Now five is a prime number , | |
| 00:44 | so we can't go any further with this , but | |
| 00:46 | 10 itself is still accomplished number . So this particular | |
| 00:49 | branch here can go further . So the numbers are | |
| 00:53 | going to 10 , we can think OK , well | |
| 00:55 | two and five go into it . So we look | |
| 00:58 | at all the dead end of our branches now . | |
| 01:00 | 52 and five are all prime numbers here . So | |
| 01:04 | what we have here , the prime factors of 50 | |
| 01:08 | here . So What are the prime factors of 50 | |
| 01:11 | ? Well , there's two major numbers here . We | |
| 01:13 | have five and we have to . So the prime | |
| 01:16 | factors of 50 is too and five . So say | |
| 01:21 | now what you asked to do is you would asked | |
| 01:24 | to work out right 50 as a product of its | |
| 01:26 | prime factors in index form . How would you go | |
| 01:29 | about doing this ? Well , it's fairly simple . | |
| 01:31 | We have the following numbers here . We can see | |
| 01:34 | that we have the following similar numbers which are five | |
| 01:37 | and five . So the way that we could write | |
| 01:39 | this is we could actually right , okay , we | |
| 01:41 | have five squared And to this we are multiplying by | |
| 01:48 | two . So in terms of 50 being written as | |
| 01:51 | a product of its prime factors in index form , | |
| 01:54 | we could write this is five squared times two because | |
| 01:56 | five squared is 25 times two Is 50 . All | |
| 02:01 | right , let's have a look at another example . | |
| 02:03 | Okay , for a second example here , we're going | |
| 02:05 | to work out the prime factors of 72 and then | |
| 02:08 | we're going to write 72 as a product of its | |
| 02:10 | prime factors in index form . So let's go about | |
| 02:13 | doing this . What number's going to 72 ? So | |
| 02:16 | the numbers are easily going to 72 that you could | |
| 02:18 | think of would be nine and 89 times eight is | |
| 02:22 | 72 . Now look at each of these branches here | |
| 02:25 | and think these guys prime or composite and because they're | |
| 02:28 | both composite , we can take these branches further nine | |
| 02:33 | , The numbers are going to this are three and | |
| 02:36 | three . You can see that both of these branches | |
| 02:38 | here now have hit their prime stage . They're not | |
| 02:40 | going to go any further in terms of eight , | |
| 02:42 | there's two numbers are going to eight . Uh well | |
| 02:45 | there's more than this , but two and four going | |
| 02:47 | to eight . Alright , so two is a prime | |
| 02:50 | number , but four is not a prime number . | |
| 02:53 | The numbers two . And to go into four and | |
| 02:57 | now what we have here is our stage of prime | |
| 02:59 | numbers for all of our branches here . So what | |
| 03:02 | have we got ? We can write down straight away | |
| 03:05 | our prime factors . What different numbers do we have | |
| 03:07 | at the end of the branches here , we have | |
| 03:08 | 3322 and a two here . So we have the | |
| 03:12 | prime factors of three and two . Now writing down | |
| 03:17 | 72 as a product of its prime factors in index | |
| 03:20 | form . Well , with our three and with her | |
| 03:22 | to how many times these guys are going to a | |
| 03:26 | power ? Okay . How many times have they been | |
| 03:28 | indexed up ? I guess you could say we have | |
| 03:30 | three times three . Okay , just twice . So | |
| 03:34 | this is three squared and we have two times two | |
| 03:37 | times two , which is three times Okay , two | |
| 03:40 | to the power of three . And these guys are | |
| 03:42 | being multiplied . So there we have it we have | |
| 03:45 | 72 written as a product of its prime factors in | |
| 03:48 | index form . So that's the way you go about | |
| 03:51 | doing this . Just go through and start writing out | |
| 03:53 | the are factors until you hit the stage where all | |
| 03:56 | the end of your branches are prime and then you | |
| 03:59 | can go through and finish what you're doing there anyway | |
| 04:03 | . Hopefully that video is a some help . We'll | |
| 04:04 | see you next time . Bye . |
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Prime Factorization is a free educational video by tecmath.
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