67 lines
1.8 KiB
Markdown
67 lines
1.8 KiB
Markdown
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---
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title: All Factors of a Number
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localeTitle: 一个数字的所有因素
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---
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## 一个数字的所有因素
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您可以将因子视为您乘以获得另一个数字的数字。
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在这种情况下，2,3,6和7都是你可以乘以得到42的所有数字。因此，它们都是42的因子。但是，它们并不是42的所有因素。为了找到所有因素，我们可以使用算法或逐步下面的过程。
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从1开始。
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1 \* 42 = 42
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1 | ...... | 42 --- | --- | ---
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试试2。
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2 \* 21 = 42
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1 | 2 | ...... | 21 | 42 --- | --- | --- | --- | ---
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试试3。
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3 \* 14 = 42
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1 | 2 | 3 | ...... | 14 | 21 | 42 --- | --- | --- | --- | --- | --- | ---
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试试4。
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没有整数可以乘以4得到42，所以我们跳过它。
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试试5。
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没有整数可以乘以5得到42，所以我们跳过它。
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试试6。
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6 \* 7 = 42
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1 | 2 | 3 | 6 | ...... | 7 | 14 | 21 | 42 --- | --- | --- | --- | --- | --- | --- | --- | ---
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由于6到7之间没有整数，所以找到了所有积极因素。上面的所有数字都可以翻转，并且将继续成为42的因子。总之，42的所有因素都在下面。
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1 | 2 | 3 | 6 | 7 | 14 | 21 | 42 | -1 | -2 | -3 | -6 | -7 | -14 | -21 | -42 --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
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## 确认因子数是否正确
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我们可以通过以下步骤快速确认我们已经确定了所有积极因素：
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1. 采用素数分解（由上面的树提供）
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2 1 \* 3 1 \* 7 \* 1
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2. 为每个指数添加一个：
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2的指数：1 + 1 = 2 3的指数：1 + 1 = 2 7的指数：1 + 1 = 2
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3. 上面的每个数字都是多个：
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2 \* 2 \* 2 = 8
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4. 确认42有8个因素：
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1 | 2 | 3 | 6 | ...... | 7 | 14 | 21 | 42 --- | --- | --- | --- | --- | --- | --- | --- | ---
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