0:00:00.000,0:00:00.730


0:00:00.730,0:00:04.180
Find all of the factors[br]of 120.

0:00:04.180,0:00:06.160
Or another way to think about[br]it, find all of the whole

0:00:06.160,0:00:09.650
numbers that 120 is[br]divisible by.

0:00:09.650,0:00:12.040
So the first one, that's[br]maybe obvious.

0:00:12.040,0:00:14.560
All whole numbers are[br]divisible by 1.

0:00:14.560,0:00:21.090
So we could write 120 is equal[br]to is to 1 times 120.

0:00:21.090,0:00:22.990
So let's write a factors[br]list over here.

0:00:22.990,0:00:26.530


0:00:26.530,0:00:28.390
So this is going to be our[br]factors list over here.

0:00:28.390,0:00:29.900
So we just found two factors.

0:00:29.900,0:00:31.910
We said, well, is it[br]divisible by 1?

0:00:31.910,0:00:33.940
Well, every whole number[br]is divisible by 1.

0:00:33.940,0:00:37.630
This is a whole number, so 1[br]is a factor at the low end.

0:00:37.630,0:00:38.490
1 is a factor.

0:00:38.490,0:00:40.580
That's its actual smallest[br]factor, and its

0:00:40.580,0:00:42.330
largest factor is 120.

0:00:42.330,0:00:46.580
You can't have something larger[br]than 120 dividing

0:00:46.580,0:00:49.500
evenly into 120.

0:00:49.500,0:00:52.400
121 will not go into 120.

0:00:52.400,0:00:54.710
So the largest factor[br]on our factors list

0:00:54.710,0:00:57.080
is going to be 120.

0:00:57.080,0:00:58.470
Now let's think about others.

0:00:58.470,0:01:02.200
Let's think about whether[br]is 2 divisible into 120?

0:01:02.200,0:01:06.910
So there's 120 equals[br]2 times something?

0:01:06.910,0:01:09.680
Well, when you look here,[br]maybe you immediately

0:01:09.680,0:01:12.760
recognize that 120 is[br]an even number.

0:01:12.760,0:01:15.000
It's ones place is a 0.

0:01:15.000,0:01:18.430
As as long as its ones place is[br]a 0, 2, 4, 6 or 8, as long

0:01:18.430,0:01:21.110
as it's an even number, the[br]whole number is even and the

0:01:21.110,0:01:23.540
whole number is divisible[br]by 2.

0:01:23.540,0:01:26.440
And to figure out what you have[br]to multiply by 2 to get

0:01:26.440,0:01:33.690
120, well, you can think of 120[br]as 12 times 10, or another

0:01:33.690,0:01:36.480
way to think about it,[br]it's 2 times 6 times

0:01:36.480,0:01:38.890
10, or 2 times 60.

0:01:38.890,0:01:40.340
You could divide it[br]out if you want.

0:01:40.340,0:01:43.690
You could say, OK,[br]2 goes into 120.

0:01:43.690,0:01:45.420
2 goes into 1 no times.

0:01:45.420,0:01:47.240
2 goes into 12 six times.

0:01:47.240,0:01:49.270
6 times 2 is 12.

0:01:49.270,0:01:50.410
Subtract.

0:01:50.410,0:01:51.100
You get 0.

0:01:51.100,0:01:52.090
Bring down the 0.

0:01:52.090,0:01:53.910
2 goes into 0 zero times.

0:01:53.910,0:01:58.010
0 times 2 is 0, and you get no[br]remainder there, so it goes

0:01:58.010,0:01:59.430
sixty times.

0:01:59.430,0:02:02.050
So we have two more factors[br]right here.

0:02:02.050,0:02:04.420
So we have the factors.

0:02:04.420,0:02:08.070
So we've established the next[br]lowest one is 2, and the next

0:02:08.070,0:02:10.110
highest factor, if we're[br]starting from the large end,

0:02:10.110,0:02:13.310
is going to be 60.

0:02:13.310,0:02:14.880
Now let's think about three.

0:02:14.880,0:02:19.780
Is 120 equal to 3[br]times something?

0:02:19.780,0:02:22.060
Well, we could just try to test[br]and divide it from the

0:02:22.060,0:02:24.410
get go, but hopefully,[br]you already know the

0:02:24.410,0:02:25.630
divisibility rule.

0:02:25.630,0:02:29.220
To figure out if something is[br]divisible by 3, you add up its

0:02:29.220,0:02:30.910
digits, and if the[br]sum is divisible

0:02:30.910,0:02:32.600
by 3, we're in business.

0:02:32.600,0:02:38.540
So if you take 120-- let[br]me do it over here.

0:02:38.540,0:02:44.180
1 plus 2 plus 0, well, that's[br]equal to 1 plus 2 is 3 plus 0

0:02:44.180,0:02:48.700
is 3, and 3 is definitely[br]divisible by 3.

0:02:48.700,0:02:52.610
So 120 is going to be[br]divisible by 3.

0:02:52.610,0:02:56.050
To figure what that number that[br]you have to multiply by 3

0:02:56.050,0:02:57.840
is, you could do it[br]in your head.

0:02:57.840,0:03:01.140
You could say, well, 3 goes into[br]12 four times, and then

0:03:01.140,0:03:04.440
you-- well, let me just do it[br]out, just in case, just for

0:03:04.440,0:03:06.030
those of you who want to[br]see it worked out.

0:03:06.030,0:03:08.090
3 goes into 12 four times.

0:03:08.090,0:03:10.570
4 times 3 is 12.

0:03:10.570,0:03:11.460
You subtract.

0:03:11.460,0:03:12.690
You're left with nothing here.

0:03:12.690,0:03:14.680
You bring down this 0.

0:03:14.680,0:03:16.730
3 goes into 0 zero times.

0:03:16.730,0:03:18.940
0 times 3 is 0.

0:03:18.940,0:03:20.510
Nothing left over.

0:03:20.510,0:03:22.077
So it goes into it[br]forty times.

0:03:22.077,0:03:24.690


0:03:24.690,0:03:28.110
And the way to think of it in[br]your head is this is the same

0:03:28.110,0:03:29.860
thing as 12 times 10.

0:03:29.860,0:03:34.280
12 divided by 3 is 4, but this[br]is going to be 4 times 10,

0:03:34.280,0:03:35.630
because you have that[br]10 left over.

0:03:35.630,0:03:36.740
Whatever works for you.

0:03:36.740,0:03:40.070
Or you can just ignore the 0,[br]divide by 3, you get a 4, and

0:03:40.070,0:03:41.290
then put the 0 back there.

0:03:41.290,0:03:42.370
Whatever works.

0:03:42.370,0:03:43.650
So we have two more factors.

0:03:43.650,0:03:50.780
At the low end, we have 3, and[br]at the high end, we have a 40.

0:03:50.780,0:03:53.600
Now, let's see if 4 divisible[br]into 120.

0:03:53.600,0:03:57.030
Now we saw the divisibility[br]rule for 4 is you ignore

0:03:57.030,0:03:59.300
everything beyond the tens[br]places and you just look at

0:03:59.300,0:04:01.040
the last two digits.

0:04:01.040,0:04:05.700
So if we're going to to think[br]about whether 4 is divisible,

0:04:05.700,0:04:07.130
you just look at the[br]last two digits.

0:04:07.130,0:04:09.130
The last two digits are 20.

0:04:09.130,0:04:13.430
20 is definitely divisible[br]by 4, so 120 will be

0:04:13.430,0:04:14.220
divisible by 4.

0:04:14.220,0:04:16.180
4 is going to be a factor.

0:04:16.180,0:04:19.250
And to figure out what we have[br]to multiply 4 by to get 120,

0:04:19.250,0:04:20.100
you could do it in your head.

0:04:20.100,0:04:23.430
You could say 12 divided[br]by 4 is 3, so 120

0:04:23.430,0:04:27.210
divided by 4 is 30.

0:04:27.210,0:04:29.890
So we have two more[br]factors: 4 and 30.

0:04:29.890,0:04:32.670
And you could work this out in[br]long division if you want to

0:04:32.670,0:04:35.940
make sure that this works out,[br]so let's keep going.

0:04:35.940,0:04:40.750
And then we have 120 is equal[br]to-- is 5 a factor?

0:04:40.750,0:04:44.630
Is 5 times something[br]equal to 120?

0:04:44.630,0:04:46.750
Well, you can't do that simple--[br]well, first of all,

0:04:46.750,0:04:48.550
we could just test[br]is it divisible?

0:04:48.550,0:04:50.650
And 120 ends with a 0.

0:04:50.650,0:04:53.400
If you end with a 0 or a 5,[br]you are divisible by 5.

0:04:53.400,0:04:55.340
So 5 definitely goes into it.

0:04:55.340,0:04:56.690
Let's figure out[br]how many times.

0:04:56.690,0:04:59.575
So 5 goes into 120.

0:04:59.575,0:05:00.830
It doesn't go into 1.

0:05:00.830,0:05:02.750
It goes into 12 two times.

0:05:02.750,0:05:04.780
2 times 5 is 10.

0:05:04.780,0:05:05.850
Subtract.

0:05:05.850,0:05:07.130
You get 2.

0:05:07.130,0:05:08.830
Bring down the 0.

0:05:08.830,0:05:11.290
5 goes into 20 four times.

0:05:11.290,0:05:18.620
4 times 5 is 20, and then you[br]subtract, and you have no left

0:05:18.620,0:05:21.120
over, as we expect, because[br]it should go in evenly.

0:05:21.120,0:05:24.760
This number ends with[br]a 0 or a 5.

0:05:24.760,0:05:27.640
Let me delete all of this so we[br]can have our scratch space

0:05:27.640,0:05:29.680
to work with later on.

0:05:29.680,0:05:33.810
So 5 times 24 is also equal[br]to 120, we have two more

0:05:33.810,0:05:37.950
factors: 5 and 24.

0:05:37.950,0:05:40.400
Let me clear up some space here[br]because I think we're

0:05:40.400,0:05:42.510
going to be dealing with[br]a lot of factors.

0:05:42.510,0:05:45.230
So let me move this[br]right here.

0:05:45.230,0:05:50.400
Let me cut it and then let me[br]paste it and move this over

0:05:50.400,0:05:53.680
here so we have more space[br]for our factors.

0:05:53.680,0:05:55.580
So we have 5 and 24.

0:05:55.580,0:05:58.590
Let's move on to 6.

0:05:58.590,0:06:02.470
So 120 is equal to[br]6 times what?

0:06:02.470,0:06:05.050
Now, to be divisible by[br]6, you have to be

0:06:05.050,0:06:07.370
divisible by 2 and 3.

0:06:07.370,0:06:09.630
Now, we know that we're already[br]divisible by 2 and 3,

0:06:09.630,0:06:12.530
so we're definitely going to[br]be divisible by 6, and you

0:06:12.530,0:06:14.140
should hopefully be able to[br]do this one in your head.

0:06:14.140,0:06:17.300
5 was a little bit harder to do[br]in your head. but 120, you

0:06:17.300,0:06:21.930
could say, well, 12 divided by 6[br]is 2, and then you have that

0:06:21.930,0:06:26.140
0 there, so 120 divided[br]by 6 would be 20.

0:06:26.140,0:06:28.550
And you could work it out in[br]long division if you like.

0:06:28.550,0:06:30.925
So 6 times 20 are two[br]more factors.

0:06:30.925,0:06:33.590


0:06:33.590,0:06:35.850
Now let's think about 7.

0:06:35.850,0:06:37.230
Let's think about 7 here.

0:06:37.230,0:06:40.490
7 is a very bizarre number, and[br]just to test it, you could

0:06:40.490,0:06:41.900
think of other ways to do it.

0:06:41.900,0:06:45.130
Let's just try to divide[br]7 into 120.

0:06:45.130,0:06:46.300
7 doesn't go into 1.

0:06:46.300,0:06:48.070
It goes into 12 one time.

0:06:48.070,0:06:50.130
1 times 7 is 7.

0:06:50.130,0:06:51.020
You subtract.

0:06:51.020,0:06:53.150
12 minus 7 is 5.

0:06:53.150,0:06:56.000
Bring down the 0.

0:06:56.000,0:06:59.610
7 times 7 is 49, so it goes[br]into it seven times.

0:06:59.610,0:07:01.650
7 times 7 is 49.

0:07:01.650,0:07:02.480
Subtract.

0:07:02.480,0:07:05.820
You have a remainder, so it[br]does not divide evenly.

0:07:05.820,0:07:07.515
So 7 does not work.

0:07:07.515,0:07:10.700


0:07:10.700,0:07:12.770
Now let's think about 8.

0:07:12.770,0:07:15.680
Let's think about[br]whether 8 works.

0:07:15.680,0:07:17.360
Let's think about 8.

0:07:17.360,0:07:18.850
I'll do the same process.

0:07:18.850,0:07:26.540
Let's take 8 into 120.

0:07:26.540,0:07:27.890
Let's just work it out.

0:07:27.890,0:07:29.640
And just as a little bit[br]of a hint-- well, I'll

0:07:29.640,0:07:30.270
just work it out.

0:07:30.270,0:07:33.390
8 goes into 12-- it doesn't[br]go into 1, so it

0:07:33.390,0:07:35.500
goes into 12 one time.

0:07:35.500,0:07:38.250
1 times 8 is 8.

0:07:38.250,0:07:39.240
Subtract there.

0:07:39.240,0:07:41.160
12 minus 8 is 4.

0:07:41.160,0:07:43.150
Bring down the 0.

0:07:43.150,0:07:45.280
8 goes into 40 five times.

0:07:45.280,0:07:49.190
5 times 8 is 40, and you're left[br]with no remainder, so it

0:07:49.190,0:07:49.940
goes evenly.

0:07:49.940,0:07:53.250
So 120-- let me get[br]rid of that.

0:07:53.250,0:08:02.630
120 is equal to 8 times 15, so[br]let's add that to our factor

0:08:02.630,0:08:09.440
list. We now have an 8[br]and now we have a 15.

0:08:09.440,0:08:11.920
Now, is it divisible by 9?

0:08:11.920,0:08:13.870
Is 120 divisible by 9?

0:08:13.870,0:08:16.300
To test that out, you just[br]add up the digits.

0:08:16.300,0:08:20.430
1 plus 2 plus 0 is equal to 3.

0:08:20.430,0:08:24.350
Well, that'll satisfy our 3[br]divisibility rule, but 3 is

0:08:24.350,0:08:27.320
not divisible by 9, so our[br]number will not be

0:08:27.320,0:08:28.700
divisible by 9.

0:08:28.700,0:08:31.380
So 9 will not work out.

0:08:31.380,0:08:32.950
9 does not work out.

0:08:32.950,0:08:34.730
So let's move on to 10.

0:08:34.730,0:08:36.450
Well, this is pretty[br]straightforward.

0:08:36.450,0:08:39.679
It ends in 0, so we will[br]be divisible by 10.

0:08:39.679,0:08:41.559
So let me write that down.

0:08:41.559,0:08:46.610
120 is equal to 10 times--[br]and this is pretty

0:08:46.610,0:08:49.780
straightforward-- 10 times 12.

0:08:49.780,0:08:51.560
This is exactly what 120 is.

0:08:51.560,0:08:53.800
It's 10 times 12, so let's[br]write those factors down.

0:08:53.800,0:08:56.500
10 and 12.

0:08:56.500,0:08:58.220
And then we have one[br]number left.

0:08:58.220,0:08:58.740
We have 11.

0:08:58.740,0:09:00.440
We don't have to go above 11,[br]because we already went

0:09:00.440,0:09:02.670
through 12, and we know that[br]there aren't any factors above

0:09:02.670,0:09:07.270
that, because we were going in[br]descending order, so we've

0:09:07.270,0:09:08.610
really filled in all the gaps.

0:09:08.610,0:09:09.830
You could try 11.

0:09:09.830,0:09:12.040
We could try it by hand,[br]if you like.

0:09:12.040,0:09:15.370
11 goes into 120-- now you know,[br]if with you know your

0:09:15.370,0:09:17.880
multiplication tables through[br]11, that this won't work, but

0:09:17.880,0:09:18.900
I'll just show you.

0:09:18.900,0:09:21.250
11 goes into 12 one time.

0:09:21.250,0:09:23.250
1 times 11 is 11.

0:09:23.250,0:09:24.630
Subtract.

0:09:24.630,0:09:26.460
1, bring down the 0.

0:09:26.460,0:09:29.010
11 goes into 10 zero times.

0:09:29.010,0:09:30.960
0 times 11 is 0.

0:09:30.960,0:09:33.500
you're left with a[br]remainder of 10.

0:09:33.500,0:09:36.150
So 11 goes into 20 ten times[br]with a remainder of 10.

0:09:36.150,0:09:37.900
It definitely does[br]not go in evenly.

0:09:37.900,0:09:45.220
So we have all of our factors[br]here: 1, 2, 3, 4, 5, 6, 8, 10,

0:09:45.220,0:09:51.260
12, 15, 20, 24, 30,[br]40, 60 and 120.

0:09:51.260,0:09:52.750
And we're done!

0:09:52.750,0:09:52.934