1 99:59:59,999 --> 99:59:59,999 因为6可以整除12 2 99:59:59,999 --> 99:59:59,999 就等于其中一个数 3 99:59:59,999 --> 99:59:59,999 就这样了 4 99:59:59,999 --> 99:59:59,999 希望你们可以解决 5 99:59:59,999 --> 99:59:59,999 并给出更多例子 6 99:59:59,999 --> 99:59:59,999 我想在不久的将来我会做另一期视频 7 99:59:59,999 --> 99:59:59,999 最大公因子或者说最大公因数的题目了 8 99:59:59,999 --> 99:59:59,999 这也讲得通 9 00:00:01,170 --> 00:00:03,364 欢迎观看最大公因子 10 00:00:03,364 --> 00:00:06,020 或者说最大公因数的视频 11 00:00:06,030 --> 00:00:09,548 首先要清楚 当一个人问你们 12 00:00:09,548 --> 00:00:16,520 12和8的最大公因子是多少？ 13 00:00:16,530 --> 00:00:22,758 或者问你们12和8的最大公因数 14 00:00:22,758 --> 00:00:25,130 是多少？ 15 00:00:25,140 --> 00:00:26,590 这个地方是c 是common的缩写 16 00:00:26,600 --> 00:00:27,563 我不知道怎么写成那样了-- 17 00:00:27,563 --> 00:00:31,014 这两个是同一个问题 18 00:00:31,014 --> 00:00:34,167 我的意思是 因子是个可以 19 00:00:34,180 --> 00:00:37,130 整除某数的数 20 00:00:37,140 --> 00:00:39,769 因数-- 我想 21 00:00:39,769 --> 00:00:41,620 它也是可以整除某数的数 22 00:00:41,620 --> 00:00:43,890 所以因子和因数是一样的 23 00:00:43,890 --> 00:00:45,960 先不说那个了 我们来算一下 24 00:00:45,970 --> 00:00:48,930 12和8的最大公因子 25 00:00:48,930 --> 00:00:52,350 或者说最大公因数 26 00:00:52,360 --> 00:00:57,250 我们要做的很简单 27 00:00:57,250 --> 00:00:59,090 首先计算出每个数的因数 28 00:00:59,100 --> 00:01:00,770 我们先写出12的 29 00:01:00,780 --> 00:01:03,950 所有因数 30 00:01:03,960 --> 00:01:06,700 1是一个 12可以被2整除 31 00:01:06,700 --> 00:01:10,220 3也可以 32 00:01:10,230 --> 00:01:11,070 4可以整除12 33 00:01:11,070 --> 00:01:12,920 5不行 34 00:01:12,930 --> 00:01:15,430 6可以 因为2×6=12 35 00:01:15,430 --> 00:01:17,600 12 当然也可以整除12 36 00:01:17,600 --> 00:01:18,940 1×12=12 37 00:01:18,950 --> 00:01:20,630 所以这些就是12的因数 38 00:01:20,640 --> 00:01:22,930 再写一下8的因数 39 00:01:22,930 --> 00:01:27,830 1可以整除8 40 00:01:27,840 --> 00:01:31,090 2也可以 41 00:01:31,090 --> 00:01:34,570 3不行 42 00:01:34,570 --> 00:01:37,000 4可以 43 00:01:37,010 --> 00:01:38,380 最后一个因数 也就是和1配对的 是8 44 00:01:38,390 --> 00:01:40,324 所以现在我们写出了12和8所有的因数 45 00:01:40,324 --> 00:01:43,490 那么接着就来找找 46 00:01:43,500 --> 00:01:47,499 它们的公因数 47 00:01:47,499 --> 00:01:51,070 1是它们两个数的公因数 48 00:01:51,070 --> 00:01:54,589 这很正常 49 00:01:54,589 --> 00:01:57,380 每个整数 50 00:01:57,390 --> 00:02:00,200 都有因数1 51 00:02:00,200 --> 00:02:01,580 它们还有公因数2 52 00:02:01,590 --> 00:02:02,820 以及4 53 00:02:02,820 --> 00:02:03,890 我们不仅对找出公因数感兴趣 54 00:02:03,900 --> 00:02:07,230 而是对最大公因数感兴趣 55 00:02:07,230 --> 00:02:09,520 它们的所有公因数是1 2和4 56 00:02:09,530 --> 00:02:14,650 最大的是哪个？ 57 00:02:14,660 --> 00:02:16,940 很简单 是4 58 00:02:16,940 --> 00:02:23,500 所以12和8的最大公因数是4 59 00:02:23,500 --> 00:02:27,718 为了强调 我写下来 60 00:02:27,718 --> 00:02:30,929 12和8的最大公因数是4 61 00:02:30,929 --> 00:02:41,891 当然 我们也可以很简单的写成 62 00:02:41,900 --> 00:02:44,170 12和8的最大公因子是4 63 00:02:44,170 --> 00:02:47,050 这样有时很有趣 64 00:02:47,060 --> 00:02:48,430 我们来做另一道题 65 00:02:48,430 --> 00:02:49,390 25和20的最大公因子 66 00:02:49,400 --> 00:02:50,150 是多少？ 67 00:02:50,150 --> 00:02:51,420 我们用同样的方法做 68 00:02:51,430 --> 00:02:52,352 25的因数是多少？ 69 00:02:52,352 --> 00:02:54,270 1是一个 70 00:02:54,280 --> 00:02:57,130 2不能整除它 71 00:02:57,130 --> 00:02:59,560 3也不行 72 00:02:59,560 --> 00:03:02,322 4不行 73 00:03:02,322 --> 00:03:07,958 5可以 74 00:03:07,958 --> 00:03:12,782 5×5=25 75 00:03:12,782 --> 00:03:21,025 最后一个是25 76 00:03:21,025 --> 00:03:22,977 25只有3个因数 这很有意思 77 00:03:22,977 --> 00:03:25,050 我会留给你们思考为什么这个数 78 00:03:25,060 --> 00:03:28,110 只有3个因数 79 00:03:28,110 --> 00:03:30,550 而其它数常常有偶数个因数 80 00:03:30,560 --> 00:03:35,638 接下来找出20的因数 81 00:03:35,638 --> 00:03:41,030 20的因数有1 2 4 5 10和20 82 00:03:41,030 --> 00:03:44,895 如果查看一下这些数 83 00:03:44,895 --> 00:03:54,687 1是它们的公因数 但这不奇怪 84 00:03:54,690 --> 00:03:56,420 但还有哪个？ 85 00:03:56,430 --> 00:03:57,330 对的 是5 86 00:03:57,330 --> 00:03:59,340 所以25和20的最大公因子或者说最大公因数 87 00:03:59,340 --> 00:04:00,283 是5 88 00:04:00,283 --> 00:04:03,378 我们再做另一道题 89 00:04:03,393 --> 00:04:05,370 5和12的最大公因数是多少？ 90 00:04:05,370 --> 00:04:06,170 5的因数是？ 91 00:04:06,180 --> 00:04:14,270 很简单 92 00:04:14,270 --> 00:04:20,520 1和5 93 00:04:20,520 --> 00:04:23,360 因为它是质数 94 00:04:23,370 --> 00:04:28,750 除了1和它本身外没有其它因数 95 00:04:28,750 --> 00:04:31,500 12的因数是？ 96 00:04:31,500 --> 00:04:35,476 12有很多因数 97 00:04:35,476 --> 00:04:37,292 1 2 3 4 6和12 98 00:04:37,292 --> 00:04:39,992 所以它们的公因数只有1 99 00:04:39,992 --> 00:04:42,880 这有些令人失望 100 00:04:42,880 --> 00:04:45,161 所以12和5的最大公因数是1 101 00:04:45,161 --> 00:04:50,190 这里我要给出一些术语 102 00:04:50,190 --> 00:04:51,680 当两个数最大公因数是1时 103 00:04:51,680 --> 00:04:56,744 它们被称作互质 104 00:04:56,744 --> 00:05:04,567 称为互质很有道理 因为质数 105 00:05:04,570 --> 00:05:05,670 的因数只有1和它本身 106 00:05:05,680 --> 00:05:08,810 两个互质的数 107 00:05:08,810 --> 00:05:11,040 最大公因数 108 00:05:11,050 --> 00:05:12,920 是1 109 00:05:12,920 --> 00:05:17,760 希望你们没被搞晕 110 00:05:17,760 --> 00:05:22,788 我们做下一道题 111 00:05:22,788 --> 00:05:24,384 求6和12的最大公因数 112 00:05:24,384 --> 00:05:29,060 我知道12出现好几次了 113 00:05:29,060 --> 00:05:33,935 我会在想数字的时候尝试着更有创造力一些 114 00:05:33,935 --> 00:05:36,350 6和12的最大公因子是？ 115 00:05:36,350 --> 00:05:39,540 6的公因数有 116 00:05:39,550 --> 00:05:42,100 1 2 3和6 117 00:05:42,100 --> 00:05:43,910 12的公因数是：1 2 3-- 118 00:05:43,920 --> 00:05:46,048 我们现在几乎可以记住了 119 00:05:46,048 --> 00:05:46,770 3 4 6和12 120 00:05:46,770 --> 00:05:49,518 1是它们的公因数 121 00:05:49,518 --> 00:05:52,600 2也是 122 00:05:52,600 --> 00:05:55,175 3是 123 00:05:55,175 --> 00:06:00,210 6也是 124 00:06:00,220 --> 00:06:01,670 所以很显然 最大公因数是多少？ 125 00:06:01,680 --> 00:06:02,906 是6 126 00:06:02,906 --> 00:06:07,710 这很有趣 127 00:06:07,720 --> 00:06:08,930 这种情况下最大公因子-- 128 00:06:08,930 --> 00:06:11,630 我承认我一直在 129 00:06:11,640 --> 00:06:12,810 因子和因数之间转换 130 00:06:12,810 --> 00:06:14,940 在数学领域应该确定使用它们二者中的一个 131 00:06:14,950 --> 00:06:18,155 6和12的最大公因子是6