0:00:01.170,0:00:03.364 Welcome to the greatest common divisor 0:00:03.364,0:00:06.020 or greatest common factor video. 0:00:06.030,0:00:09.548 So just to be clear, first of all, when someone asks you 0:00:09.548,0:00:16.520 what's the greatest common divisor of twelve and eight? 0:00:16.530,0:00:22.758 Or they ask you what's the greatest common factor of twelve and eight? 0:00:22.758,0:00:25.130 That's a c right there for common. 0:00:25.140,0:00:26.590 I don't know why it came out like that. 0:00:26.600,0:00:27.563 They're asking you the same thing. 0:00:27.563,0:00:31.014 I mean, really a divisor is just a number that can divide into something, 0:00:31.014,0:00:34.167 and a factor-- well, I think, that's also a number that can divide into something. 0:00:34.180,0:00:37.130 So a divisor and a factor are kind of the same thing. 0:00:37.140,0:00:39.769 So with that out of the way, let's figure out, 0:00:39.769,0:00:41.620 what is the greatest common divisor 0:00:41.620,0:00:43.890 or the greatest common factor of twelve and eight? 0:00:43.890,0:00:45.960 Well, what we do is, it's pretty straightforward. 0:00:45.970,0:00:48.930 First we just figure out the factors of each of the numbers. 0:00:48.930,0:00:52.350 So first let's write all of the factors out of the number twelve. 0:00:52.360,0:00:57.250 Well, one is a factor. Two goes into twelve. 0:00:57.250,0:00:59.090 Three goes into twelve. 0:00:59.100,0:01:00.770 Four goes into twelve. 0:01:00.780,0:01:03.950 Five does not to go into twelve. 0:01:03.960,0:01:06.700 Six goes into twelve because two times six. 0:01:06.700,0:01:10.220 And then, twelve goes into twelve of course. 0:01:10.230,0:01:11.070 One times twelve. 0:01:11.070,0:01:12.920 So that's the factors of twelve. 0:01:12.930,0:01:15.430 Let's write the factors of eight. 0:01:15.430,0:01:17.600 Well, one goes into eight. 0:01:17.600,0:01:18.940 Two goes into eight. 0:01:18.950,0:01:20.630 Three does not go into eight. 0:01:20.640,0:01:22.930 Four does go into eight. 0:01:22.930,0:01:27.830 And then the last factor, pairing up with the one is eight. 0:01:27.840,0:01:31.090 So now we've written all the factors of twelve and eight. 0:01:31.090,0:01:34.570 So let's figure out what the common factors of twelve and eight are. 0:01:34.570,0:01:37.000 Well, they both have the common factor of one. 0:01:37.010,0:01:38.380 And that's really not so special. 0:01:38.390,0:01:40.324 Pretty much every whole number 0:01:40.324,0:01:43.490 or every integer has the common factor of one. 0:01:43.500,0:01:47.499 They both share the common factor two 0:01:47.499,0:01:51.070 and they both share the common factor four. 0:01:51.070,0:01:54.589 So we're not just interested in finding a common factor, 0:01:54.589,0:01:57.380 we're interested in finding the greatest common factor. 0:01:57.390,0:02:00.200 So all the common factors are one, two and four. 0:02:00.200,0:02:01.580 And what's the greatest of them? 0:02:01.590,0:02:02.820 Well, that's pretty easy. 0:02:02.820,0:02:03.890 It's four. 0:02:03.900,0:02:07.230 So the greatest common factor of twelve and eight is four. 0:02:07.230,0:02:09.520 Let me write that down just for emphasis. 0:02:09.530,0:02:14.650 Greatest common factor of twelve and eight equals four. 0:02:14.660,0:02:16.940 And of course, we could have just as easily had said, 0:02:16.940,0:02:23.500 the greatest common divisor of twelve and eight equals four. 0:02:23.500,0:02:27.718 Sometimes it does things a little funny. 0:02:27.718,0:02:30.929 Let's do another problem. 0:02:30.929,0:02:41.891 What is the greatest common divisor of twenty-five and twenty? 0:02:41.900,0:02:44.170 Well, let's do it the same way. 0:02:44.170,0:02:47.050 The factors of twenty-five? 0:02:47.060,0:02:48.430 Well, it's one. 0:02:48.430,0:02:49.390 Two doesn't go into it. 0:02:49.400,0:02:50.150 Three doesn't go into it. 0:02:50.150,0:02:51.420 Four doesn't go into it. 0:02:51.430,0:02:52.352 Five does. 0:02:52.352,0:02:54.270 It's actually five times five. 0:02:54.280,0:02:57.130 And then twenty-five. 0:02:57.130,0:02:59.560 It's interesting that this only has three factors. 0:02:59.560,0:03:02.322 I'll leave you to think about why this number only has three factors 0:03:02.322,0:03:07.958 and other numbers tend to have an even number of factors. 0:03:07.958,0:03:12.782 And then now we do the factors of twenty. 0:03:12.782,0:03:21.025 Factors of twenty are one, two, four, five, ten, and twenty. 0:03:21.025,0:03:22.977 And if we just look at this by inspection we see, 0:03:22.977,0:03:25.050 well, they both share one, but that's nothing special. 0:03:25.060,0:03:28.110 But they both have the common factor of? 0:03:28.110,0:03:30.550 You got it-- five. 0:03:30.560,0:03:35.638 So the greatest common divisor or greatest common factor 0:03:35.638,0:03:41.030 of twenty-five and twenty, well, that equals five. 0:03:41.030,0:03:44.895 Let's do another problem. 0:03:44.895,0:03:54.687 What is the greatest common factor of five and twelve? 0:03:54.690,0:03:56.420 Well, factors of five? 0:03:56.430,0:03:57.330 Pretty easy. 0:03:57.330,0:03:59.340 One and five. 0:03:59.340,0:04:00.283 That's because it's a prime number. 0:04:00.283,0:04:03.378 It has no factors other than one and itself. 0:04:03.393,0:04:05.370 Then the factors of twelve? 0:04:05.370,0:04:06.170 Twelve has a lot of factors. 0:04:06.180,0:04:14.270 It's one, two, three, four, six, and twelve. 0:04:14.270,0:04:20.520 So it really looks like only common factor they share is one. 0:04:20.520,0:04:23.360 So that was, I guess, in some ways kind of disappointing. 0:04:23.370,0:04:28.750 So the greatest common factor of five and twelve is one. 0:04:28.750,0:04:31.500 And I'll throw out some terminology here for you. 0:04:31.500,0:04:35.476 When two numbers have a greatest common factor of only one, 0:04:35.476,0:04:37.292 they're called relatively prime. 0:04:37.292,0:04:39.992 And that kind of makes sense because a prime number 0:04:39.992,0:04:42.880 is something that only has one and itself as a factor. 0:04:42.880,0:04:45.161 And two relatively prime numbers 0:04:45.161,0:04:50.190 are numbers that only have one as their greatest common factor. 0:04:50.190,0:04:51.680 Hope I didn't confuse you. 0:04:51.680,0:04:56.744 Let's do another problem. 0:04:56.744,0:05:04.567 Let's do the greatest common divisor of six and twelve. 0:05:04.570,0:05:05.670 I know twelve's coming up a lot. 0:05:05.680,0:05:08.810 I'll try to be more creative when I think of my numbers. 0:05:08.810,0:05:11.040 Well, the greatest common divisor of six and twelve? 0:05:11.050,0:05:12.920 Well, it's the factors of six. 0:05:12.920,0:05:17.760 Are one, two, three, and six. 0:05:17.760,0:05:22.788 Factors of twelve: one, two, three-- 0:05:22.788,0:05:24.384 we almost should have these memorized by now. 0:05:24.384,0:05:29.060 Three, four, six, and twelve. 0:05:29.060,0:05:33.935 Well, it turns out one is a common factor of both. 0:05:33.935,0:05:36.350 Two is also a common factor of both. 0:05:36.350,0:05:39.540 Three is a common factor of both. 0:05:39.550,0:05:42.100 And six is a common factor of both. 0:05:42.100,0:05:43.910 And of course, what's the greatest common factor? 0:05:43.920,0:05:46.048 Well, it's six. 0:05:46.048,0:05:46.770 And that's interesting. 0:05:46.770,0:05:49.518 So in this situation the greatest common divisor-- 0:05:49.518,0:05:52.600 and I apologize that I keep switching between divisor and factor. 0:05:52.600,0:05:55.175 The mathematics community should settle on one of the two. 0:05:55.175,0:06:00.210 The greatest common divisor of six and twelve equals six. 0:06:00.220,0:06:01.670 So it actually equals one of the numbers. 0:06:01.680,0:06:02.906 And that makes a lot of sense 0:06:02.906,0:06:07.710 because six actually is divisible into twelve. 0:06:07.720,0:06:08.930 Well, that's it for now. 0:06:08.930,0:06:11.630 Hopefully you're ready to do the greatest common divisor 0:06:11.640,0:06:12.810 or factor problems. 0:06:12.810,0:06:14.940 I think I might make another module in the near future 0:06:14.950,0:06:18.155 that'll give you more example problems.