1
00:00:00,730 --> 00:00:04,180
我們來找出120所有的因數

2
00:00:04,180 --> 00:00:06,160
或者換個方式想

3
00:00:06,160 --> 00:00:09,650
找出所有120可以被整除的數字

4
00:00:09,650 --> 00:00:12,040
第一個數字很明顯

5
00:00:12,040 --> 00:00:14,560
所有數字都可以被1整除

6
00:00:14,560 --> 00:00:21,090
因此，我們可以寫120等於是1乘以120

7
00:00:21,090 --> 00:00:22,990
讓我們把所有因數列在這裡

8
00:00:26,530 --> 00:00:28,390
所有因數列在這裡

9
00:00:28,390 --> 00:00:29,900
目前我們發現了兩個因數

10
00:00:29,900 --> 00:00:31,910
好了，是否能被1整除？

11
00:00:31,910 --> 00:00:33,940
所有數字都能被1整除

12
00:00:33,940 --> 00:00:37,630
所以1是一個最小的因素數

13
00:00:37,630 --> 00:00:38,490
1是一個因數

14
00:00:38,490 --> 00:00:40,580
1是最小的因數

15
00:00:40,580 --> 00:00:42,330
而最大的因數是120

16
00:00:42,330 --> 00:00:46,580
你不能有數字大於120

17
00:00:46,580 --> 00:00:49,500
而被120整除

18
00:00:49,500 --> 00:00:52,400
121不會被120整除

19
00:00:52,400 --> 00:00:54,710
因此我們最大的因數

20
00:00:54,710 --> 00:00:57,080
將是120

21
00:00:57,080 --> 00:00:58,470
現在讓我們想想別的數字

22
00:00:58,470 --> 00:01:02,200
讓我們來想想是否2可以被120整除

23
00:01:02,200 --> 00:01:06,910
有120等於2乘以的東西嗎

24
00:01:06,910 --> 00:01:09,680
當你看到這裡

25
00:01:09,680 --> 00:01:12,760
你馬上認識到120是一個偶數

26
00:01:12,760 --> 00:01:15,000
它的個位數是0

27
00:01:15,000 --> 00:01:18,430
只要個位數是0，2，4，6或8

28
00:01:18,430 --> 00:01:21,110
它是一個偶數

29
00:01:21,110 --> 00:01:23,540
偶數是可以被2整除的整數

30
00:01:23,540 --> 00:01:26,440
有什麼乘以2可以得到120

31
00:01:26,440 --> 00:01:33,690
你可以認為想成120的12乘以10倍，或

32
00:01:33,690 --> 00:01:36,480
或想成2乘以6乘以10

33
00:01:36,480 --> 00:01:38,890
或2乘以60

34
00:01:38,890 --> 00:01:40,340
你可以實際除看看

35
00:01:40,340 --> 00:01:43,690
120除以2

36
00:01:43,690 --> 00:01:45,420
1不能被2除

37
00:01:45,420 --> 00:01:47,240
12被2除等於6

38
00:01:47,240 --> 00:01:49,270
6乘以2為12

39
00:01:49,270 --> 00:01:50,410
減以後

40
00:01:50,410 --> 00:01:51,100
你得到0

41
00:01:51,100 --> 00:01:52,090
0拉下來

42
00:01:52,090 --> 00:01:53,910
0除以2等於0

43
00:01:53,910 --> 00:01:58,010
0乘以2為0，沒有餘數

44
00:01:58,010 --> 00:01:59,430
所以是60

45
00:01:59,430 --> 00:02:02,050
因此我們又有兩個因數

46
00:02:02,050 --> 00:02:04,420
我們又多兩個因數

47
00:02:04,420 --> 00:02:08,070
下一個最低的因數是2

48
00:02:08,070 --> 00:02:10,110
下一個最高的因數

49
00:02:10,110 --> 00:02:13,310
是60

50
00:02:13,310 --> 00:02:14,880
現在，讓我們考慮3

51
00:02:14,880 --> 00:02:19,780
有120等於3乘以的東西嗎

52
00:02:19,780 --> 00:02:22,060
我們可以試著實際試除看看

53
00:02:22,060 --> 00:02:24,410
但我希望你已經知道了

54
00:02:24,410 --> 00:02:25,630
3的可除性規則

55
00:02:25,630 --> 00:02:29,220
為了知道數字可不可以被3整除

56
00:02:29,220 --> 00:02:30,910
你把它的位數總和加起來

57
00:02:30,910 --> 00:02:32,600
如果可以被3整除就對了

58
00:02:32,600 --> 00:02:38,540
讓我在這裡把120 的位數總和加起來

59
00:02:38,540 --> 00:02:44,180
1加2加0是3

60
00:02:44,180 --> 00:02:48,700
3是可以被3整除的

61
00:02:48,700 --> 00:02:52,610
所以120可以被3整除

62
00:02:52,610 --> 00:02:56,050
120等於3乘以什麽東西呢

63
00:02:56,050 --> 00:02:57,840
你可以用心算的

64
00:02:57,840 --> 00:03:01,140
好了，12等於是3乘以4

65
00:03:01,140 --> 00:03:04,440
好，讓我實際除出來

66
00:03:04,440 --> 00:03:06,030
希望你可以看到它怎麼做

67
00:03:06,030 --> 00:03:08,090
12除以3等於4

68
00:03:08,090 --> 00:03:10,570
4乘以3等於12

69
00:03:10,570 --> 00:03:11,460
減去以後

70
00:03:11,460 --> 00:03:12,690
沒有餘數留下

71
00:03:12,690 --> 00:03:14,680
0拉下來

72
00:03:14,680 --> 00:03:16,730
0除以3等於0

73
00:03:16,730 --> 00:03:18,940
0乘以3為0

74
00:03:18,940 --> 00:03:20,510
沒有餘數留下

75
00:03:20,510 --> 00:03:22,077
所以是3乘以40

76
00:03:24,690 --> 00:03:28,110
用心算的可以想成

77
00:03:28,110 --> 00:03:29,860
12乘以10

78
00:03:29,860 --> 00:03:34,280
12除以3是4

79
00:03:34,280 --> 00:03:35,630
4乘以10,因為你有10留下來,

80
00:03:35,630 --> 00:03:36,740
這樣可以

81
00:03:36,740 --> 00:03:40,070
或者你可以先忽略為0，除以3你會得到一個4

82
00:03:40,070 --> 00:03:41,290
然後把0放回來

83
00:03:41,290 --> 00:03:42,370
這樣也可以

84
00:03:42,370 --> 00:03:43,650
現在我們又有了兩個因數

85
00:03:43,650 --> 00:03:50,780
在底端我們有3，而在上端我們有一個40。

86
00:03:50,780 --> 00:03:53,600
現在來看看，120可不可以被4整除

87
00:03:53,600 --> 00:03:57,030
4的 可除性規則

88
00:03:57,030 --> 00:03:59,300
是你忽略十位數以上的一切

89
00:03:59,300 --> 00:04:01,040
只要看最後兩位數字

90
00:04:01,040 --> 00:04:05,700
如果我們要考慮是否可以被4整除

91
00:04:05,700 --> 00:04:07,130
你只要看看在最後兩位數字

92
00:04:07,130 --> 00:04:09,130
最後兩位數是20

93
00:04:09,130 --> 00:04:13,430
20肯定是可以被4整除

94
00:04:13,430 --> 00:04:14,220
所以120可以被4整除

95
00:04:14,220 --> 00:04:16,180
4將是一個因數

96
00:04:16,180 --> 00:04:19,250
我們必須找出有什麼乘以4可以得到120

97
00:04:19,250 --> 00:04:20,100
你可以用心算的

98
00:04:20,100 --> 00:04:23,430
你可以說12除以4是3

99
00:04:23,430 --> 00:04:27,210
所以120除以4是30

100
00:04:27,210 --> 00:04:29,890
因此，我們有兩個因數：4和30

101
00:04:29,890 --> 00:04:32,670
你也可以實際除出來確認

102
00:04:32,670 --> 00:04:35,940
讓我們繼續

103
00:04:35,940 --> 00:04:40,750
5是120的 一個因數嗎？

104
00:04:40,750 --> 00:04:44,630
120等於5乘以什麽東西嗎？

105
00:04:44,630 --> 00:04:46,750
好，首先

106
00:04:46,750 --> 00:04:48,550
我們可以實際看看

107
00:04:48,550 --> 00:04:50,650
120個位數是0

108
00:04:50,650 --> 00:04:53,400
如果個位數是0或5，是可以被5整除

109
00:04:53,400 --> 00:04:55,340
因此5可以

110
00:04:55,340 --> 00:04:56,690
讓我們弄清楚是乘以什麽

111
00:04:56,690 --> 00:04:59,575
120除以5

112
00:04:59,575 --> 00:05:00,830
1太小

113
00:05:00,830 --> 00:05:02,750
12除以5等於2

114
00:05:02,750 --> 00:05:04,780
2乘以5是10

115
00:05:05,850 --> 00:05:07,130
減後剩下2

116
00:05:07,130 --> 00:05:08,830
0拉下來

117
00:05:08,830 --> 00:05:11,290
20除以5等於4

118
00:05:11,290 --> 00:05:18,620
4乘5是20，減後沒有餘數

119
00:05:18,620 --> 00:05:21,120
正如我們的預期可以整除

120
00:05:21,120 --> 00:05:24,760
因為個位數是0或5

121
00:05:24,760 --> 00:05:27,640
讓我先擦掉

122
00:05:27,640 --> 00:05:29,680
等下才有地方

123
00:05:29,680 --> 00:05:33,810
5乘以24等於120，

124
00:05:33,810 --> 00:05:37,950
我們有兩個因數：5和24

125
00:05:37,950 --> 00:05:40,400
讓我清理一些地方

126
00:05:40,400 --> 00:05:42,510
因為因數將要有很多

127
00:05:42,510 --> 00:05:45,230
所以，讓我這裡搬一下

128
00:05:45,230 --> 00:05:50,400
讓我將他搬到這裡

129
00:05:50,400 --> 00:05:53,680
我們才有更多的空間

130
00:05:53,680 --> 00:05:55,580
我們有5和24

131
00:05:55,580 --> 00:05:58,590
讓我們繼續到6

132
00:05:58,590 --> 00:06:02,470
120是等於6乘以什麼

133
00:06:02,470 --> 00:06:05,050
要可以被6整除

134
00:06:05,050 --> 00:06:07,370
你必須要可以2和3整除

135
00:06:07,370 --> 00:06:09,630
可以我們已經知道120可以2和3整除

136
00:06:09,630 --> 00:06:12,530
所以我們肯定120會被6整除

137
00:06:12,530 --> 00:06:14,140
你應該可以用心算的

138
00:06:14,140 --> 00:06:17,300
5心算做一點點起來難

139
00:06:17,300 --> 00:06:21,930
但12除以6是2

140
00:06:21,930 --> 00:06:26,140
所以120除以6 是20

141
00:06:26,140 --> 00:06:28,550
如果你喜歡你可以實際除除

142
00:06:28,550 --> 00:06:30,925
因此6和20是兩個因數

143
00:06:33,590 --> 00:06:35,850
現在想想7

144
00:06:35,850 --> 00:06:37,230
讓我們來想想7

145
00:06:37,230 --> 00:06:40,490
7是一個非常奇怪的數字

146
00:06:40,490 --> 00:06:41,900
你可以想其他的方法來做

147
00:06:41,900 --> 00:06:45,130
讓我們嘗試120除以 7

148
00:06:45,130 --> 00:06:46,300
1太小

149
00:06:46,300 --> 00:06:48,070
12除以7等於1

150
00:06:48,070 --> 00:06:50,130
1乘以7是7

151
00:06:50,130 --> 00:06:51,020
減

152
00:06:51,020 --> 00:06:53,150
12減去7是5

153
00:06:53,150 --> 00:06:56,000
0拉下來

154
00:06:56,000 --> 00:06:59,610
7乘以7為49,所以7

155
00:06:59,610 --> 00:07:01,650
所以7乘以7為49

156
00:07:01,650 --> 00:07:02,480
減法

157
00:07:02,480 --> 00:07:05,820
減後你有餘數，

158
00:07:05,820 --> 00:07:07,515
所以7不整除

159
00:07:10,700 --> 00:07:12,770
現在讓我們想想8

160
00:07:12,770 --> 00:07:15,680
讓我們來想想8是否整除

161
00:07:17,360 --> 00:07:18,850
做同樣的過程

162
00:07:18,850 --> 00:07:26,540
120除以8

163
00:07:26,540 --> 00:07:27,890
我們來做

164
00:07:27,890 --> 00:07:29,640
給你一點點的提示 -

165
00:07:29,640 --> 00:07:30,270
好吧我們先做

166
00:07:30,270 --> 00:07:33,390
1太小

167
00:07:33,390 --> 00:07:35,500
12除以8等於1

168
00:07:35,500 --> 00:07:38,250
1乘以8是8

169
00:07:38,250 --> 00:07:39,240
減。

170
00:07:39,240 --> 00:07:41,160
12減8是4

171
00:07:41,160 --> 00:07:43,150
0拉下來

172
00:07:43,150 --> 00:07:45,280
40除以8等於5

173
00:07:45,280 --> 00:07:49,190
5乘以8是40，沒有餘數

174
00:07:49,190 --> 00:07:49,940
所以可以整除

175
00:07:49,940 --> 00:07:53,250
因此，120 -擦一下

176
00:07:53,250 --> 00:08:02,630
120等於8乘以15，加到我們的因數表

177
00:08:02,630 --> 00:08:09,440
我們有一個8，有一個15

178
00:08:09,440 --> 00:08:11,920
現在，它可以被9整除?

179
00:08:11,920 --> 00:08:13,870
120 可以被9整除?

180
00:08:13,870 --> 00:08:16,300
要測試，你只需要加位數總和

181
00:08:16,300 --> 00:08:20,430
1加2加0是等於3

182
00:08:20,430 --> 00:08:24,350
這滿足我們3的可除性規則

183
00:08:24,350 --> 00:08:27,320
但不滿足9的可除性規則

184
00:08:27,320 --> 00:08:28,700
所以不可以被9整除

185
00:08:28,700 --> 00:08:31,380
所以9不可以

186
00:08:31,380 --> 00:08:32,950
9不可以

187
00:08:32,950 --> 00:08:34,730
讓我們繼續進到10

188
00:08:34,730 --> 00:08:36,450
這非常簡單

189
00:08:36,450 --> 00:08:39,679
個位數是0，因此將被10整除

190
00:08:39,679 --> 00:08:41,559
讓我把它寫下來

191
00:08:41,559 --> 00:08:46,610
120等於10乘以多少

192
00:08:46,610 --> 00:08:49,780
-這是非常簡單的 -10乘以12

193
00:08:49,780 --> 00:08:51,560
這正是120

194
00:08:51,560 --> 00:08:53,800
這是10乘以12，讓我們寫下這些因數

195
00:08:53,800 --> 00:08:56,500
10和12

196
00:08:56,500 --> 00:08:58,220
然後我們剩下一個數字

197
00:08:58,220 --> 00:08:58,740
我們還有11

198
00:08:58,740 --> 00:09:00,440
我們不用考慮11以上，因為我們已經做了12

199
00:09:00,440 --> 00:09:02,670
我們知道12以上沒有任何因數

200
00:09:02,670 --> 00:09:07,270
因為我們從大到小排列

201
00:09:07,270 --> 00:09:08,610
所以我們確實填了所有的空隙

202
00:09:08,610 --> 00:09:09,830
你可以試試11

203
00:09:09,830 --> 00:09:12,040
如果你喜歡我們可以試試手算

204
00:09:12,040 --> 00:09:15,370
120除以11 - 你現在應該知道乘法表了

205
00:09:15,370 --> 00:09:17,880
11將無法整除

206
00:09:17,880 --> 00:09:18,900
我就用手算

207
00:09:18,900 --> 00:09:21,250
12除以11等於1

208
00:09:21,250 --> 00:09:23,250
1乘以 11等於11

209
00:09:23,250 --> 00:09:24,630
減法

210
00:09:24,630 --> 00:09:26,460
剩下1，0拉下來

211
00:09:26,460 --> 00:09:29,010
10除以11等於0

212
00:09:29,010 --> 00:09:30,960
0乘以 11等於0

213
00:09:30,960 --> 00:09:33,500
你留下了個餘數 10

214
00:09:33,500 --> 00:09:36,150
10除以11等於0，餘數是 10

215
00:09:36,150 --> 00:09:37,900
絕對無法整除

216
00:09:37,900 --> 00:09:45,220
因此我們有所有的因數：1，2，3，4，5，6，8，10，

217
00:09:45,220 --> 00:09:51,260
12，15，20，24，30，40，60和120。

218
00:09:51,260 --> 00:09:52,750
我們大功告成了