1
00:00:00,000 --> 00:00:00,730


2
00:00:00,730 --> 00:00:04,180
Find all of the factors
of 120.

3
00:00:04,180 --> 00:00:06,160
Or another way to think about
it, find all of the whole

4
00:00:06,160 --> 00:00:09,650
numbers that 120 is
divisible by.

5
00:00:09,650 --> 00:00:12,040
So the first one, that's
maybe obvious.

6
00:00:12,040 --> 00:00:14,560
All whole numbers are
divisible by 1.

7
00:00:14,560 --> 00:00:21,090
So we could write 120 is equal
to is to 1 times 120.

8
00:00:21,090 --> 00:00:22,990
So let's write a factors
list over here.

9
00:00:22,990 --> 00:00:26,530


10
00:00:26,530 --> 00:00:28,390
So this is going to be our
factors list over here.

11
00:00:28,390 --> 00:00:29,900
So we just found two factors.

12
00:00:29,900 --> 00:00:31,910
We said, well, is it
divisible by 1?

13
00:00:31,910 --> 00:00:33,940
Well, every whole number
is divisible by 1.

14
00:00:33,940 --> 00:00:37,630
This is a whole number, so 1
is a factor at the low end.

15
00:00:37,630 --> 00:00:38,490
1 is a factor.

16
00:00:38,490 --> 00:00:40,580
That's its actual smallest
factor, and its

17
00:00:40,580 --> 00:00:42,330
largest factor is 120.

18
00:00:42,330 --> 00:00:46,580
You can't have something larger
than 120 dividing

19
00:00:46,580 --> 00:00:49,500
evenly into 120.

20
00:00:49,500 --> 00:00:52,400
121 will not go into 120.

21
00:00:52,400 --> 00:00:54,710
So the largest factor
on our factors list

22
00:00:54,710 --> 00:00:57,080
is going to be 120.

23
00:00:57,080 --> 00:00:58,470
Now let's think about others.

24
00:00:58,470 --> 00:01:02,200
Let's think about whether
is 2 divisible into 120?

25
00:01:02,200 --> 00:01:06,910
So there's 120 equals
2 times something?

26
00:01:06,910 --> 00:01:09,680
Well, when you look here,
maybe you immediately

27
00:01:09,680 --> 00:01:12,760
recognize that 120 is
an even number.

28
00:01:12,760 --> 00:01:15,000
It's ones place is a 0.

29
00:01:15,000 --> 00:01:18,430
As as long as its ones place is
a 0, 2, 4, 6 or 8, as long

30
00:01:18,430 --> 00:01:21,110
as it's an even number, the
whole number is even and the

31
00:01:21,110 --> 00:01:23,540
whole number is divisible
by 2.

32
00:01:23,540 --> 00:01:26,440
And to figure out what you have
to multiply by 2 to get

33
00:01:26,440 --> 00:01:33,690
120, well, you can think of 120
as 12 times 10, or another

34
00:01:33,690 --> 00:01:36,480
way to think about it,
it's 2 times 6 times

35
00:01:36,480 --> 00:01:38,890
10, or 2 times 60.

36
00:01:38,890 --> 00:01:40,340
You could divide it
out if you want.

37
00:01:40,340 --> 00:01:43,690
You could say, OK,
2 goes into 120.

38
00:01:43,690 --> 00:01:45,420
2 goes into 1 no times.

39
00:01:45,420 --> 00:01:47,240
2 goes into 12 six times.

40
00:01:47,240 --> 00:01:49,270
6 times 2 is 12.

41
00:01:49,270 --> 00:01:50,410
Subtract.

42
00:01:50,410 --> 00:01:51,100
You get 0.

43
00:01:51,100 --> 00:01:52,090
Bring down the 0.

44
00:01:52,090 --> 00:01:53,910
2 goes into 0 zero times.

45
00:01:53,910 --> 00:01:58,010
0 times 2 is 0, and you get no
remainder there, so it goes

46
00:01:58,010 --> 00:01:59,430
sixty times.

47
00:01:59,430 --> 00:02:02,050
So we have two more factors
right here.

48
00:02:02,050 --> 00:02:04,420
So we have the factors.

49
00:02:04,420 --> 00:02:08,070
So we've established the next
lowest one is 2, and the next

50
00:02:08,070 --> 00:02:10,110
highest factor, if we're
starting from the large end,

51
00:02:10,110 --> 00:02:13,310
is going to be 60.

52
00:02:13,310 --> 00:02:14,880
Now let's think about three.

53
00:02:14,880 --> 00:02:19,780
Is 120 equal to 3
times something?

54
00:02:19,780 --> 00:02:22,060
Well, we could just try to test
and divide it from the

55
00:02:22,060 --> 00:02:24,410
get go, but hopefully,
you already know the

56
00:02:24,410 --> 00:02:25,630
divisibility rule.

57
00:02:25,630 --> 00:02:29,220
To figure out if something is
divisible by 3, you add up its

58
00:02:29,220 --> 00:02:30,910
digits, and if the
sum is divisible

59
00:02:30,910 --> 00:02:32,600
by 3, we're in business.

60
00:02:32,600 --> 00:02:38,540
So if you take 120-- let
me do it over here.

61
00:02:38,540 --> 00:02:44,180
1 plus 2 plus 0, well, that's
equal to 1 plus 2 is 3 plus 0

62
00:02:44,180 --> 00:02:48,700
is 3, and 3 is definitely
divisible by 3.

63
00:02:48,700 --> 00:02:52,610
So 120 is going to be
divisible by 3.

64
00:02:52,610 --> 00:02:56,050
To figure what that number that
you have to multiply by 3

65
00:02:56,050 --> 00:02:57,840
is, you could do it
in your head.

66
00:02:57,840 --> 00:03:01,140
You could say, well, 3 goes into
12 four times, and then

67
00:03:01,140 --> 00:03:04,440
you-- well, let me just do it
out, just in case, just for

68
00:03:04,440 --> 00:03:06,030
those of you who want to
see it worked out.

69
00:03:06,030 --> 00:03:08,090
3 goes into 12 four times.

70
00:03:08,090 --> 00:03:10,570
4 times 3 is 12.

71
00:03:10,570 --> 00:03:11,460
You subtract.

72
00:03:11,460 --> 00:03:12,690
You're left with nothing here.

73
00:03:12,690 --> 00:03:14,680
You bring down this 0.

74
00:03:14,680 --> 00:03:16,730
3 goes into 0 zero times.

75
00:03:16,730 --> 00:03:18,940
0 times 3 is 0.

76
00:03:18,940 --> 00:03:20,510
Nothing left over.

77
00:03:20,510 --> 00:03:22,077
So it goes into it
forty times.

78
00:03:22,077 --> 00:03:24,690


79
00:03:24,690 --> 00:03:28,110
And the way to think of it in
your head is this is the same

80
00:03:28,110 --> 00:03:29,860
thing as 12 times 10.

81
00:03:29,860 --> 00:03:34,280
12 divided by 3 is 4, but this
is going to be 4 times 10,

82
00:03:34,280 --> 00:03:35,630
because you have that
10 left over.

83
00:03:35,630 --> 00:03:36,740
Whatever works for you.

84
00:03:36,740 --> 00:03:40,070
Or you can just ignore the 0,
divide by 3, you get a 4, and

85
00:03:40,070 --> 00:03:41,290
then put the 0 back there.

86
00:03:41,290 --> 00:03:42,370
Whatever works.

87
00:03:42,370 --> 00:03:43,650
So we have two more factors.

88
00:03:43,650 --> 00:03:50,780
At the low end, we have 3, and
at the high end, we have a 40.

89
00:03:50,780 --> 00:03:53,600
Now, let's see if 4 divisible
into 120.

90
00:03:53,600 --> 00:03:57,030
Now we saw the divisibility
rule for 4 is you ignore

91
00:03:57,030 --> 00:03:59,300
everything beyond the tens
places and you just look at

92
00:03:59,300 --> 00:04:01,040
the last two digits.

93
00:04:01,040 --> 00:04:05,700
So if we're going to to think
about whether 4 is divisible,

94
00:04:05,700 --> 00:04:07,130
you just look at the
last two digits.

95
00:04:07,130 --> 00:04:09,130
The last two digits are 20.

96
00:04:09,130 --> 00:04:13,430
20 is definitely divisible
by 4, so 120 will be

97
00:04:13,430 --> 00:04:14,220
divisible by 4.

98
00:04:14,220 --> 00:04:16,180
4 is going to be a factor.

99
00:04:16,180 --> 00:04:19,250
And to figure out what we have
to multiply 4 by to get 120,

100
00:04:19,250 --> 00:04:20,100
you could do it in your head.

101
00:04:20,100 --> 00:04:23,430
You could say 12 divided
by 4 is 3, so 120

102
00:04:23,430 --> 00:04:27,210
divided by 4 is 30.

103
00:04:27,210 --> 00:04:29,890
So we have two more
factors: 4 and 30.

104
00:04:29,890 --> 00:04:32,670
And you could work this out in
long division if you want to

105
00:04:32,670 --> 00:04:35,940
make sure that this works out,
so let's keep going.

106
00:04:35,940 --> 00:04:40,750
And then we have 120 is equal
to-- is 5 a factor?

107
00:04:40,750 --> 00:04:44,630
Is 5 times something
equal to 120?

108
00:04:44,630 --> 00:04:46,750
Well, you can't do that simple--
well, first of all,

109
00:04:46,750 --> 00:04:48,550
we could just test
is it divisible?

110
00:04:48,550 --> 00:04:50,650
And 120 ends with a 0.

111
00:04:50,650 --> 00:04:53,400
If you end with a 0 or a 5,
you are divisible by 5.

112
00:04:53,400 --> 00:04:55,340
So 5 definitely goes into it.

113
00:04:55,340 --> 00:04:56,690
Let's figure out
how many times.

114
00:04:56,690 --> 00:04:59,575
So 5 goes into 120.

115
00:04:59,575 --> 00:05:00,830
It doesn't go into 1.

116
00:05:00,830 --> 00:05:02,750
It goes into 12 two times.

117
00:05:02,750 --> 00:05:04,780
2 times 5 is 10.

118
00:05:04,780 --> 00:05:05,850
Subtract.

119
00:05:05,850 --> 00:05:07,130
You get 2.

120
00:05:07,130 --> 00:05:08,830
Bring down the 0.

121
00:05:08,830 --> 00:05:11,290
5 goes into 20 four times.

122
00:05:11,290 --> 00:05:18,620
4 times 5 is 20, and then you
subtract, and you have no left

123
00:05:18,620 --> 00:05:21,120
over, as we expect, because
it should go in evenly.

124
00:05:21,120 --> 00:05:24,760
This number ends with
a 0 or a 5.

125
00:05:24,760 --> 00:05:27,640
Let me delete all of this so we
can have our scratch space

126
00:05:27,640 --> 00:05:29,680
to work with later on.

127
00:05:29,680 --> 00:05:33,810
So 5 times 24 is also equal
to 120, we have two more

128
00:05:33,810 --> 00:05:37,950
factors: 5 and 24.

129
00:05:37,950 --> 00:05:40,400
Let me clear up some space here
because I think we're

130
00:05:40,400 --> 00:05:42,510
going to be dealing with
a lot of factors.

131
00:05:42,510 --> 00:05:45,230
So let me move this
right here.

132
00:05:45,230 --> 00:05:50,400
Let me cut it and then let me
paste it and move this over

133
00:05:50,400 --> 00:05:53,680
here so we have more space
for our factors.

134
00:05:53,680 --> 00:05:55,580
So we have 5 and 24.

135
00:05:55,580 --> 00:05:58,590
Let's move on to 6.

136
00:05:58,590 --> 00:06:02,470
So 120 is equal to
6 times what?

137
00:06:02,470 --> 00:06:05,050
Now, to be divisible by
6, you have to be

138
00:06:05,050 --> 00:06:07,370
divisible by 2 and 3.

139
00:06:07,370 --> 00:06:09,630
Now, we know that we're already
divisible by 2 and 3,

140
00:06:09,630 --> 00:06:12,530
so we're definitely going to
be divisible by 6, and you

141
00:06:12,530 --> 00:06:14,140
should hopefully be able to
do this one in your head.

142
00:06:14,140 --> 00:06:17,300
5 was a little bit harder to do
in your head. but 120, you

143
00:06:17,300 --> 00:06:21,930
could say, well, 12 divided by 6
is 2, and then you have that

144
00:06:21,930 --> 00:06:26,140
0 there, so 120 divided
by 6 would be 20.

145
00:06:26,140 --> 00:06:28,550
And you could work it out in
long division if you like.

146
00:06:28,550 --> 00:06:30,925
So 6 times 20 are two
more factors.

147
00:06:30,925 --> 00:06:33,590


148
00:06:33,590 --> 00:06:35,850
Now let's think about 7.

149
00:06:35,850 --> 00:06:37,230
Let's think about 7 here.

150
00:06:37,230 --> 00:06:40,490
7 is a very bizarre number, and
just to test it, you could

151
00:06:40,490 --> 00:06:41,900
think of other ways to do it.

152
00:06:41,900 --> 00:06:45,130
Let's just try to divide
7 into 120.

153
00:06:45,130 --> 00:06:46,300
7 doesn't go into 1.

154
00:06:46,300 --> 00:06:48,070
It goes into 12 one time.

155
00:06:48,070 --> 00:06:50,130
1 times 7 is 7.

156
00:06:50,130 --> 00:06:51,020
You subtract.

157
00:06:51,020 --> 00:06:53,150
12 minus 7 is 5.

158
00:06:53,150 --> 00:06:56,000
Bring down the 0.

159
00:06:56,000 --> 00:06:59,610
7 times 7 is 49, so it goes
into it seven times.

160
00:06:59,610 --> 00:07:01,650
7 times 7 is 49.

161
00:07:01,650 --> 00:07:02,480
Subtract.

162
00:07:02,480 --> 00:07:05,820
You have a remainder, so it
does not divide evenly.

163
00:07:05,820 --> 00:07:07,515
So 7 does not work.

164
00:07:07,515 --> 00:07:10,700


165
00:07:10,700 --> 00:07:12,770
Now let's think about 8.

166
00:07:12,770 --> 00:07:15,680
Let's think about
whether 8 works.

167
00:07:15,680 --> 00:07:17,360
Let's think about 8.

168
00:07:17,360 --> 00:07:18,850
I'll do the same process.

169
00:07:18,850 --> 00:07:26,540
Let's take 8 into 120.

170
00:07:26,540 --> 00:07:27,890
Let's just work it out.

171
00:07:27,890 --> 00:07:29,640
And just as a little bit
of a hint-- well, I'll

172
00:07:29,640 --> 00:07:30,270
just work it out.

173
00:07:30,270 --> 00:07:33,390
8 goes into 12-- it doesn't
go into 1, so it

174
00:07:33,390 --> 00:07:35,500
goes into 12 one time.

175
00:07:35,500 --> 00:07:38,250
1 times 8 is 8.

176
00:07:38,250 --> 00:07:39,240
Subtract there.

177
00:07:39,240 --> 00:07:41,160
12 minus 8 is 4.

178
00:07:41,160 --> 00:07:43,150
Bring down the 0.

179
00:07:43,150 --> 00:07:45,280
8 goes into 40 five times.

180
00:07:45,280 --> 00:07:49,190
5 times 8 is 40, and you're left
with no remainder, so it

181
00:07:49,190 --> 00:07:49,940
goes evenly.

182
00:07:49,940 --> 00:07:53,250
So 120-- let me get
rid of that.

183
00:07:53,250 --> 00:08:02,630
120 is equal to 8 times 15, so
let's add that to our factor

184
00:08:02,630 --> 00:08:09,440
list. We now have an 8
and now we have a 15.

185
00:08:09,440 --> 00:08:11,920
Now, is it divisible by 9?

186
00:08:11,920 --> 00:08:13,870
Is 120 divisible by 9?

187
00:08:13,870 --> 00:08:16,300
To test that out, you just
add up the digits.

188
00:08:16,300 --> 00:08:20,430
1 plus 2 plus 0 is equal to 3.

189
00:08:20,430 --> 00:08:24,350
Well, that'll satisfy our 3
divisibility rule, but 3 is

190
00:08:24,350 --> 00:08:27,320
not divisible by 9, so our
number will not be

191
00:08:27,320 --> 00:08:28,700
divisible by 9.

192
00:08:28,700 --> 00:08:31,380
So 9 will not work out.

193
00:08:31,380 --> 00:08:32,950
9 does not work out.

194
00:08:32,950 --> 00:08:34,730
So let's move on to 10.

195
00:08:34,730 --> 00:08:36,450
Well, this is pretty
straightforward.

196
00:08:36,450 --> 00:08:39,679
It ends in 0, so we will
be divisible by 10.

197
00:08:39,679 --> 00:08:41,559
So let me write that down.

198
00:08:41,559 --> 00:08:46,610
120 is equal to 10 times--
and this is pretty

199
00:08:46,610 --> 00:08:49,780
straightforward-- 10 times 12.

200
00:08:49,780 --> 00:08:51,560
This is exactly what 120 is.

201
00:08:51,560 --> 00:08:53,800
It's 10 times 12, so let's
write those factors down.

202
00:08:53,800 --> 00:08:56,500
10 and 12.

203
00:08:56,500 --> 00:08:58,220
And then we have one
number left.

204
00:08:58,220 --> 00:08:58,740
We have 11.

205
00:08:58,740 --> 00:09:00,440
We don't have to go above 11,
because we already went

206
00:09:00,440 --> 00:09:02,670
through 12, and we know that
there aren't any factors above

207
00:09:02,670 --> 00:09:07,270
that, because we were going in
descending order, so we've

208
00:09:07,270 --> 00:09:08,610
really filled in all the gaps.

209
00:09:08,610 --> 00:09:09,830
You could try 11.

210
00:09:09,830 --> 00:09:12,040
We could try it by hand,
if you like.

211
00:09:12,040 --> 00:09:15,370
11 goes into 120-- now you know,
if with you know your

212
00:09:15,370 --> 00:09:17,880
multiplication tables through
11, that this won't work, but

213
00:09:17,880 --> 00:09:18,900
I'll just show you.

214
00:09:18,900 --> 00:09:21,250
11 goes into 12 one time.

215
00:09:21,250 --> 00:09:23,250
1 times 11 is 11.

216
00:09:23,250 --> 00:09:24,630
Subtract.

217
00:09:24,630 --> 00:09:26,460
1, bring down the 0.

218
00:09:26,460 --> 00:09:29,010
11 goes into 10 zero times.

219
00:09:29,010 --> 00:09:30,960
0 times 11 is 0.

220
00:09:30,960 --> 00:09:33,500
you're left with a
remainder of 10.

221
00:09:33,500 --> 00:09:36,150
So 11 goes into 20 ten times
with a remainder of 10.

222
00:09:36,150 --> 00:09:37,900
It definitely does
not go in evenly.

223
00:09:37,900 --> 00:09:45,220
So we have all of our factors
here: 1, 2, 3, 4, 5, 6, 8, 10,

224
00:09:45,220 --> 00:09:51,260
12, 15, 20, 24, 30,
40, 60 and 120.

225
00:09:51,260 --> 00:09:52,750
And we're done!

226
00:09:52,750 --> 00:09:52,934