5.3质数和合数

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  质数和合数

  

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  Simon is working on a riddle.
  ::西蒙正在研究一个谜题

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  “I am a number between 1 and 50. The  sum  of my digits is not  prime , but I myself am prime. In a year, you will only see me 7 times. What number am I?”
  ::“我是1到50之间的数字,我的数字总和不是正数,但我自己是正数。一年之内,你只看到我7次。我算什么数字?”

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  How can Simon solve the riddle?
  ::西蒙怎么解开谜语?

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  In this concept, you will learn how to classify a number as a prime or composite number.
  ::在此概念中,您将学习如何将数字分类为质数或复合数。

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  Classifying Prime and Composite Numbers
  ::分类主数和综合数字

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  Numbers can be classified into two categories. The number of  factors  that a number has determines whether the number is considered a  prime number  or a  composite number .
  ::数字可分为两类。数字决定数字是质数还是复合数的因素数。

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  Prime numbers are special numbers that are greater than 1 and only have two factors: 1 and the prime number itself. Composite numbers are numbers that have more than two factors. Most numbers are composite numbers.
  ::位数是特殊数字,大于1,只有两个因素:1和质数本身。综合数字是有两个以上因素的数字。大多数数字是复合数字。

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  Here is a prime number.
  ::这是质数。

  13

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  The factors of 13 are only 1 and 13. Therefore, 13 is a prime number. Here is a chart of prime numbers. There are 25 prime numbers between 1 and 100. Take a few minutes to take some notes on prime and composite numbers. Be particularly careful when considering the number “1”. One is neither prime nor composite.
  ::13个因素只有1个和13个因素。 因此, 13个是质数。 这是质数图。 质数图是25个质数, 介数在1到100之间。 质数和合成数需要几分钟来做一些笔记。 考虑数字“ 1 ” 时要特别小心。 一个人既不是质数,也不是质数。

  

  [Figure 2]

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  Here is a composite number.
  ::这是一个复合数字。

  44

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  The factors for 44 is 1, 2, 4, 11, 22, and 44. Therefore, 44 is a composite number; it is made up of more than two factors.
  ::44的系数是1、2、4、11、22和44,因此,44是一个复合数字;它由两个以上因素组成。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Simon’s riddle.
  ::先前,你对西蒙的谜题感到疑惑。

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  Use the prime number cart to help solve the riddle. “I am a number between 1 and 50. The sum of my digits is not prime, but I myself am prime. In a year, you will only see me 7 times. What number am I?
  ::使用质数车帮助解开谜题 。 “ 我是一个在1到50之间的数字。 我的数字总和不是质数,但我自己是质数。 一年后,你只看到我7次。 我是什么数字?

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  First, look at the numbers between 1 an 50 that are prime. There are 15 prime numbers.
  ::首先,看看在1比50之间是质数。有15个质数。

  $$\begin{array}{r}2,3,5,7,11,13,17,19,23,29,31,37,41,43,47\end{array}$$

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  Then, eliminate the numbers where the sum of the digits is prime.
  ::然后,删除数字数之和的正数。

  $$\begin{array}{r}\cancel{2},\cancel{3},\cancel{5},\cancel{7},\cancel{11},13,17,19,\cancel{23},\cancel{29},31,37,\cancel{41},\cancel{43},\cancel{47}\end{array}$$

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  Next, find the number you only see 7 times a year. Think about a calendar. 37 is not on a calendar at all. You see 11, 13, 17, 19 more than 7 times in a year.
  ::接下来, 找到您每年只看到7次的号码。 想想一个日历。 37 完全不在日历上。 您每年看到11, 13, 17, 19, 超过7次 。

  $$\begin{array}{r}\cancel{2},\cancel{3},\cancel{5},\cancel{7},\cancel{11},\cancel{13},\cancel{17},\cancel{19},\cancel{23},\cancel{29},\mathbf{31},\cancel{37},\cancel{41},\cancel{43},\cancel{47}\end{array}$$

   

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  The answer to the riddle is 31.
  ::谜题的答案是31

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  Example 2
  ::例2

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  Prove that 91 is a prime number.
  ::证明91是质数

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  First, list all the factors of 91. 91 at the very least has the factors 1 and 91. Keep looking for other factors.
  ::首先,列出91.91的所有因素,其中至少有因素1和91。 继续寻找其他因素。

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  Not 2, 3, 4, 5, 6. Let’s  divide  91 by 7.
  ::我们把91除以7

  $$\begin{array}{r}91÷7=13\end{array}$$

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  91 also has the factors 7 and 13.
  ::91 还有因素7和13。

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  91 is not a prime number. It is a composite number.
  ::91不是质数,而是复合数。

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  Example 3
  ::例3

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  If a number has more than two factors, the number is prime. True or false?
  ::如果一个数字有两个以上因素,数字是关键因素。是真实的还是虚假的?

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  False, numbers with more than two factors are composite numbers.
  ::假数字,有两个以上因素的数字是复合数字。

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  Example 4
  ::例4

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  The operation associated with factors is addition. True or false?
  ::与因素有关的操作是附加的,是真实的还是虚假的?

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  False, the operation associated with factors is multiplication.
  ::假的,与因素有关的操作是乘法。

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  Example 5
  ::例5

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  Why is 29 a prime number?
  ::为什么29是质数?

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  29 is a prime number because the only two factors for 29 are 1 and 29.
  ::29是一个质数,因为29中唯一的两个因素是1和29。

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  Review
  ::回顾

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  Identify the following values as prime or composite.
  ::确定下列数值为主值或复合值。

  1. 12
  2. 10
  3. 15
  4. 16
  5. 56
  6. 18
  7. 20
  8. 22
  9. 23
  10. 25
  11. 27
  12. 31
  13. 81
  14. 48
  15. 24
  16. 30

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源