1
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寫出75的質因數分解式

2
00:00:04,160 --> 00:00:07,390
要求用指數法表示

3
00:00:07,390 --> 00:00:08,970
這裡有幾點有趣之處

4
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質因數分解以及指數記數法

5
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我們稍後再考慮指數記數法

6
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所以首先我們要考慮的是

7
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什麽是質數

8
00:00:19,380 --> 00:00:22,240
作爲複習 質數是

9
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只能被1和它本身整除的數

10
00:00:26,130 --> 00:00:28,880
舉個例子--

11
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我寫一些數

12
00:00:34,760 --> 00:00:36,840
質數 非質數

13
00:00:36,840 --> 00:00:39,850
2是一個質數

14
00:00:39,850 --> 00:00:42,490
它只被1和2整除

15
00:00:42,490 --> 00:00:46,790
3是一個質數

16
00:00:46,790 --> 00:00:49,790
4不是 因爲它可以被1 2和4整除

17
00:00:49,790 --> 00:00:50,580
我們可以繼續

18
00:00:50,580 --> 00:00:56,220
5 5只被1和5整除 所以5是質數

19
00:00:56,220 --> 00:00:59,920
6不是質數 因爲它可以被2和3整除

20
00:00:59,920 --> 00:01:01,590
我想你們大致了解了

21
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到7了 7是質數

22
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它只被1和7整除

23
00:01:06,470 --> 00:01:08,220
8不是質數

24
00:01:08,220 --> 00:01:11,440
也許你們會說9是質數 但記住

25
00:01:11,440 --> 00:01:15,420
它可以被3整除 所以9也不是

26
00:01:15,420 --> 00:01:18,970
質數和奇數不是一個概念

27
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再看10 10也不是質數

28
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它可以被2和5整除

29
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11 它只被1和11整除

30
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所以11是個質數

31
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我們可以一直往後數

32
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人們已經寫出了尋找最大質數的

33
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電腦程序

34
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既然現在我們知道質數是什麽了

35
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那麽其實質因數分解就是把一個數

36
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比如75 分解成一係列質數

37
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我們試著做一下

38
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從75開始 我用一種被稱爲

39
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因數分解樹的方法來做

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首先我們試著找出

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75所有因數中最小的質數

42
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最小的質數是2

43
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75能被2整除嗎？

44
00:01:57,390 --> 00:02:00,705
75是奇數 或者說因爲個位上是5

45
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所以是奇數

46
00:02:02,280 --> 00:02:06,580
5不能被2整除 所以75也不能被2整除

47
00:02:06,580 --> 00:02:08,090
接下來試試3

48
00:02:08,090 --> 00:02:09,639
75能被3整除嗎？

49
00:02:09,639 --> 00:02:12,440
7+5=12

50
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12可以被3整除

51
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所以75等於3乘以某數

52
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如果你們曾經找過零錢

53
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你們就知道 如果有3/4美元

54
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也就是75美分 或者說3×25

55
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這就得到了75

56
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所以75=3×25

57
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如果你們不信 可以把它乘出來

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算一下3×25

59
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現在 25能被-- 你們可以不用考慮2

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如果75不被2整除

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那25也不可以

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但或許25可以被3整除

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把各位相加 2+5 是7

64
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7不被3整除 所以25也不行

65
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繼續 5

66
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25被5整除嗎？

67
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當然

68
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它等於5×5

69
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25=5×5

70
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這樣因數分解就做完了

71
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因爲現在得出了所有的質數

72
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所以我們可以寫出來 75=3×5×5

73
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75=3×5×5

74
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可以說是3×25

75
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因爲25=5×5

76
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3×25 25=5×5

77
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那麽這就是質因數分解

78
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但題目要求我們用指數記數法

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表示答案

80
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也就是說 如果有重覆的質數

81
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可以把它們寫成指數

82
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5×5是多少？

83
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5×5是它自身乘兩次

84
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也就等於5^2

85
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所以如果我們要把答案用指數記數法表示