Section outline

  • lesson content

    Mara is in making flower arrangements for a party. She has 48 carnations and 42 daisies. She wants there to be an equal number of carnations and daisies in each bouquet. What is the most number of bouquets she can make? How many of each flower will they contain?
    ::玛拉为派对安排花朵。 她有48个康乃馨和42个菊花。 她希望每朵花里都有相同数量的康乃馨和菊花。 她能做的花束最多吗? 每朵花里有多少花?

    In this concept, you will learn to find the greatest common  factors  of numbers using lists.
    ::在这个概念中,你们将学会使用清单找到最大的共同数字因素。

    Finding The Greatest Common Factor Using Lists
    ::寻找使用名单的最大共同因素

    The   (GCF)  is the greatest factor that two or more numbers have in common. One way to find the GCF is to make lists of the factors for two numbers and then choose the greatest factor that the two factors have in common.
    :sadGCF)是两个或两个以上数字共有的最大因素,找到绿色气候基金的一个办法是列出两个数字的系数,然后选择两个因素共有的最大因素。

    Find the GCF for 12 and 16. It is helpful to  order  them from smallest to largest in order to make sure that you cover every factor.
    ::确定全球合作框架的期限为12年和16年,将其从最小改为最大是有益的,以确保你涵盖每个因素。

    First, find all the factors of 12 and 16 and write them in a list in the order of least to greatest.
    ::首先,找出12和16的所有因素,把它们写在一份清单中,其顺序最少到最多。

    12 − 1 , 2 , 3 , 4 , 6 , 12 16 − 1 , 2 , 4 , 8 , 16

    One way to check if all the factors are listed is to use the rainbow method. Draw a line from one part of a factor pair to the other. The resulting image should resemble a rainbow.
    ::检查是否列出所有因素的方法之一是使用彩虹方法。从一个要素对对的一个部分绘制一条线到另一个要素对的一个部分。由此生成的图像应该与彩虹相似。

    lesson content

    Next, identify the GCF, the largest number that appears in both lists. The GCF for 12 and 16 is 4.
    ::其次,确定绿色气候基金,这是两个清单中数目最多的全球合作框架,12个和16个全球合作框架为4个。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Mara and her flowers.
    ::之前,你得到一个问题 关于玛拉和她的花。

    Mara has 48 carnations and 42 daisies and wants each bouquet to have the same number of flowers. Compare the factors 48 and 42 and find the greatest common factor.
    ::Mara有48个康乃馨和42个菊花,希望每个花束花朵数量相同,比较因素48和42,发现最大的共同因素。

    First, find all the factors of 48 and 42 and write them from least to greatest.
    ::首先,找出所有48和42的因素,从最少到最多写出来。

    48 − 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 48 42 − 1 , 2 , 3 , 6 , 7 , 14 , 21 , 42

    Then, identify the GCF. The GCF for 48 and 42 is 6.
    ::然后,确定绿色气候基金。48和42的绿色气候基金是6。

    Next, find the number of carnations and daisies in 6 bouquets.
    ::接下来,在6个花束中找到康乃馨和花菊的数量。

    carnations :   48 ÷ 6 = 8 daisies : 42 ÷ 6 = 7

    The most number of bouquets Mara can make will be 6. Each will have 8 carnations and 7 daisies.
    ::最多能做的花束是6个 每个有8个康乃馨和7个菊花

    Example 2
    ::例2

    What is the GCF of 140 and 124?
    ::140和124的全球合作框架是什么?

    First, find all the factors of 140 and 124 and write them in a list in the order of least to greatest.
    ::首先,找出140和124的所有因数,把它们写进一份清单,其顺序最少到最多。

    140 − 1 , 2 , 4 _ , 5 , 7 , 10 , 14 , 20 , 28 , 35 , 70 , 140 124 − 1 , 2 , 4 _ , 31 , 62 , 124

    Next, identify the GCF, the largest number that appears in both lists. The GCF for 140 and 124 is 4.
    ::其次,确定绿色气候基金,这是两个清单中数目最多的全球合作框架,140个全球合作框架和124个全球合作框架分别为4个。

    Example 3
    ::例3

    Find the GCF for the pair of numbers.
    ::为数字寻找绿色气候基金。

    24  and  36

    First, find all the factors of 24 and 36 and write them in a list in the order of least to greatest.
    ::首先,找到24和36的所有因素,把它们写进一份清单中,其顺序最少到最多。

    24 − 1 , 2 , 3 , 4 , 6 , 8 , 12 _ , 24 36 − 1 , 2 , 3 , 4 , 6 , 9 , 12 _ , 18 , 36

    Next, identify the GCF, the largest number that appears in both lists. The GCF for 24 and 36 is 12.
    ::其次,确定绿色气候基金,这是两个清单中数目最多的全球合作框架,24个和36个全球合作框架为12个。

    Example 4
    ::例4

    Find the GCF for the pair of numbers.
    ::为数字寻找绿色气候基金。

    10  and  18

    First, find all the factors of 10 and 18 and write them in a list in the order of least to greatest.
    ::首先,找出10和18的所有因素,把它们写在一份清单中,以最少至最大的顺序排列。

    10 − 1 , 2 _ , 5 , 10 18 − 1 , 2 _ , 3 , 6 , 9 , 18

    Next, identify the GCF, the largest number that appears in both lists. The GCF for 10 and 18 is 2.
    ::其次,确定绿色气候基金,这是两个清单中最大的一个,10个和18个绿色气候基金为2个。

    Example 5
    ::例5

    Find the GCF for the pair of numbers.
    ::为数字寻找绿色气候基金。

    18  and  45
     

    First, find all the factors of 18 and 45 and write them in a list in the order of least to greatest.
    ::首先,找到所有18和45的因数, 把它们写在一份清单中, 以最少至最大的因数排列。

    18 − 1 , 2 , 3 , 6 , 9 _ , 18 45 − 1 , 3 , 5 , 9 _ , 25 , 45

    Next, identify the GCF, the largest number that appears in both lists. The GCF for 18 and 45 is 9.
    ::其次,确定绿色气候基金,这是两个清单中数目最多的全球合作框架,18个和45个全球合作框架为9个。

    Review
    ::回顾

    Find the GCF for each pair of numbers.
    ::为每一对数字寻找绿色气候基金。

    1. 9 and 21
      ::9和21
    2. 4 and 16
      ::第4和16条
    3. 6 and 8
      ::第六条和第八条
    4. 12 and 22
      ::12和22
    5. 24 and 30
      ::24和30
    6. 35 and 47
      ::35和47
    7. 35 and 50
      ::35和50
    8. 44 and 121
      ::44和121
    9. 48 and 144
      ::48和144
    10. 60 and 75
      ::60和75
    11. 21 and 13
      ::21和13
    12. 14 and 35
      ::14和35
    13. 81 and 36
      ::81和36
    14. 90 and 80
      ::90和80)
    15. 22 and 33
      ::22和33
    16. 11 and 13
      ::11和13
    17. 15 and 30
      ::第15和30段
    18. 28 and 63
      ::28和63
    19. 67 and 14
      ::67和14
    20. 18 and 36
      ::18和36

    Review (Answers) 
    ::回顾(答复)

    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 。

    Resources
    ::资源