WEBVTT

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我們來找出120所有的因數

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或者換個方式想

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找出所有120可以被整除的數字

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第一個數字很明顯

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所有數字都可以被1整除

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因此，我們可以寫120等於是1乘以120

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讓我們把所有因數列在這裡

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所有因數列在這裡

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目前我們發現了兩個因數

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好了，是否能被1整除？

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所有數字都能被1整除

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所以1是一個最小的因素數

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1是一個因數

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1是最小的因數

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而最大的因數是120

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你不能有數字大於120

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而被120整除

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121不會被120整除

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因此我們最大的因數

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將是120

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現在讓我們想想別的數字

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讓我們來想想是否2可以被120整除

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有120等於2乘以的東西嗎

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當你看到這裡

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你馬上認識到120是一個偶數

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它的個位數是0

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只要個位數是0，2，4，6或8

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它是一個偶數

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偶數是可以被2整除的整數

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有什麼乘以2可以得到120

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你可以認為想成120的12乘以10倍，或

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或想成2乘以6乘以10

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或2乘以60

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你可以實際除看看

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120除以2

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1不能被2除

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12被2除等於6

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6乘以2為12

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減以後

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你得到0

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0拉下來

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0除以2等於0

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0乘以2為0，沒有餘數

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所以是60

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因此我們又有兩個因數

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我們又多兩個因數

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下一個最低的因數是2

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下一個最高的因數

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是60

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現在，讓我們考慮3

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有120等於3乘以的東西嗎

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我們可以試著實際試除看看

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但我希望你已經知道了

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3的可除性規則

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為了知道數字可不可以被3整除

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你把它的位數總和加起來

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如果可以被3整除就對了

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讓我在這裡把120 的位數總和加起來

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1加2加0是3

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3是可以被3整除的

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所以120可以被3整除

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120等於3乘以什麽東西呢

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你可以用心算的

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好了，12等於是3乘以4

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好，讓我實際除出來

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希望你可以看到它怎麼做

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12除以3等於4

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4乘以3等於12

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減去以後

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沒有餘數留下

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0拉下來

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0除以3等於0

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0乘以3為0

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沒有餘數留下

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所以是3乘以40

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用心算的可以想成

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12乘以10

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12除以3是4

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4乘以10,因為你有10留下來,

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這樣可以

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或者你可以先忽略為0，除以3你會得到一個4

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然後把0放回來

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這樣也可以

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現在我們又有了兩個因數

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在底端我們有3，而在上端我們有一個40。

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現在來看看，120可不可以被4整除

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4的 可除性規則

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是你忽略十位數以上的一切

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只要看最後兩位數字

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如果我們要考慮是否可以被4整除

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你只要看看在最後兩位數字

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最後兩位數是20

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20肯定是可以被4整除

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所以120可以被4整除

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4將是一個因數

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我們必須找出有什麼乘以4可以得到120

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你可以用心算的

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你可以說12除以4是3

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所以120除以4是30

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因此，我們有兩個因數：4和30

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你也可以實際除出來確認

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讓我們繼續

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5是120的 一個因數嗎？

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120等於5乘以什麽東西嗎？

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好，首先

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我們可以實際看看

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120個位數是0

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如果個位數是0或5，是可以被5整除

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因此5可以

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讓我們弄清楚是乘以什麽

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120除以5

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1太小

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12除以5等於2

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2乘以5是10

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減後剩下2

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0拉下來

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20除以5等於4

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4乘5是20，減後沒有餘數

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正如我們的預期可以整除

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因為個位數是0或5

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讓我先擦掉

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等下才有地方

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5乘以24等於120，

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我們有兩個因數：5和24

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讓我清理一些地方

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因為因數將要有很多

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所以，讓我這裡搬一下

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讓我將他搬到這裡

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我們才有更多的空間

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我們有5和24

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讓我們繼續到6

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120是等於6乘以什麼

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要可以被6整除

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你必須要可以2和3整除

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可以我們已經知道120可以2和3整除

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所以我們肯定120會被6整除

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你應該可以用心算的

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5心算做一點點起來難

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但12除以6是2

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所以120除以6 是20

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如果你喜歡你可以實際除除

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因此6和20是兩個因數

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現在想想7

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讓我們來想想7

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7是一個非常奇怪的數字

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你可以想其他的方法來做

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讓我們嘗試120除以 7

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1太小

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12除以7等於1

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1乘以7是7

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減

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12減去7是5

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0拉下來

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7乘以7為49,所以7

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所以7乘以7為49

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減法

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減後你有餘數，

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所以7不整除

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現在讓我們想想8

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讓我們來想想8是否整除

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做同樣的過程

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120除以8

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我們來做

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給你一點點的提示 -

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好吧我們先做

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1太小

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12除以8等於1

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1乘以8是8

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減。

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12減8是4

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0拉下來

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40除以8等於5

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5乘以8是40，沒有餘數

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所以可以整除

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因此，120 -擦一下

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120等於8乘以15，加到我們的因數表

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我們有一個8，有一個15

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現在，它可以被9整除?

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120 可以被9整除?

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要測試，你只需要加位數總和

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1加2加0是等於3

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這滿足我們3的可除性規則

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但不滿足9的可除性規則

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所以不可以被9整除

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所以9不可以

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9不可以

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讓我們繼續進到10

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這非常簡單

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個位數是0，因此將被10整除

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讓我把它寫下來

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120等於10乘以多少

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-這是非常簡單的 -10乘以12

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這正是120

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這是10乘以12，讓我們寫下這些因數

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10和12

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然後我們剩下一個數字

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我們還有11

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我們不用考慮11以上，因為我們已經做了12

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我們知道12以上沒有任何因數

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因為我們從大到小排列

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所以我們確實填了所有的空隙

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你可以試試11

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如果你喜歡我們可以試試手算

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120除以11 - 你現在應該知道乘法表了

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11將無法整除

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我就用手算

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12除以11等於1

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1乘以 11等於11

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減法

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剩下1，0拉下來

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10除以11等於0

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0乘以 11等於0

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你留下了個餘數 10

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10除以11等於0，餘數是 10

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絕對無法整除

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因此我們有所有的因數：1，2，3，4，5，6，8，10，

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12，15，20，24，30，40，60和120。

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我們大功告成了