path: root/Save_Mathematics/P6/map611m11/map611m11a02/a.txt

<p>
 <span style="font-weight: bold;">
  Guided Practice.
  <br />
  <br />
 </span>
 Example1: The Highest Common Devisor.
 <br />
 <br />
 a. Find the devisors of 24.
 <br style="font-weight: bold;" />
 <br style="font-weight: bold;" />
 <span style="font-weight: bold;">
  Solution:
 </span>
 <br />
 1;2;3;4;6;8;12and 24 because 24/1=24 ;24/2=12; 24/3=8; 24/4=6; 24/6=4;24/8=3; 24/12=2; 24/24=24 thus the devisors of 24 are 8 which are: 1;2;3;4;6;8;12and 24.
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 <br />
 b. Find the devisors of 54.
 <br style="font-weight: bold;" />
 <br style="font-weight: bold;" />
 <span style="font-weight: bold;">
  Solution:
 </span>
 <br />
 1;2;3;6;9;18;27 and 54 because 54/1=54; 54/2=27;54/3=18; 54/9=6; 54/18=3; 54/27=2; 54/54=1
 <br />
 thus the devisors of 54 are 8 which are 1;2;3;6;9;18;27 and 54
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 <br />
 Example2: Find the Highest Common devisor of 24 and 54
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 <br />
 <span style="font-weight: bold;">
  Solution:
 </span>
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 <br />
 <span style="font-weight: bold;">
  Method 1:
 </span>
 <br />
 a) Find the factors of 24=
 <span style="font-weight: bold;">
  1;2;3
 </span>
 ;4;
 <span style="font-weight: bold;">
  6
 </span>
 ;8;12;24
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 b) Find the factors of 54=
 <span style="font-weight: bold;">
  1;2;3;6
 </span>
 ;9;27;54
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 The Common Devisors of 24and 54 aree 1;2;3 and 6.
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 so, the highest Common Devisor of 24 and 54 is 6
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 <span style="font-weight: bold;">
  Methode 2:
 </span>
 <br />
 Deviding by Lowest Common devisor.
</p>
<table border="1" width="100%">
 <tbody>
  <tr>
   <td width="33%" valign="top">
    Number1
    <br />
   </td>
   <td width="33%" valign="top">
    Number2
    <br />
   </td>
   <td width="33%" valign="top">
    Common devisors
    <br />
   </td>
  </tr>
  <tr>
   <td width="33%" valign="top">
    24
    <br />
   </td>
   <td width="33%" valign="top">
    54
    <br />
   </td>
   <td width="33%" valign="top">
    2
    <br />
   </td>
  </tr>
  <tr>
   <td width="33%" valign="top">
    12
    <br />
   </td>
   <td width="33%" valign="top">
    27
    <br />
   </td>
   <td width="33%" valign="top">
    3
    <br />
   </td>
  </tr>
  <tr>
   <td style="vertical-align: top;">
    4
    <br />
   </td>
   <td style="vertical-align: top;">
    9
    <br />
   </td>
   <td style="vertical-align: top;">
    <br />
   </td>
  </tr>
 </tbody>
</table>
<p>
 <br />
 The Higheest Common Devidor is 2*3=6
 <br />
 <br />
 Example3: Find the HCD of this set of numbers.
 <br />
 24;36;60 and 96
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 <br />
 <span style="font-weight: bold;">
  Solution:
 </span>
 <br />
 Methode 1:
 <br />
 a) The factors of 24=
 <span style="font-weight: bold;">
  1;2;3;4;6;8;12
 </span>
 ;24
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 b) The factors of 36=
 <span style="font-weight: bold;">
  1;2;3;4;6
 </span>
 ;9;
 <span style="font-weight: bold;">
  12
 </span>
 ;18;36
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 c) The factors of 60 =
 <span style="font-weight: bold;">
  1;2;3;4
 </span>
 ;5;
 <span style="font-weight: bold;">
  6;
 </span>
 10;
 <span style="font-weight: bold;">
  12
 </span>
 ;15;20;30;60
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 d) The factors of 96=
 <span style="font-weight: bold;">
  1;2;3;4;6
 </span>
 ;8;
 <span style="font-weight: bold;">
  12;
 </span>
 16;24;32;48;96
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 <br />
 The common devisors of 24;36;60 and 96 are 1;2;3;4;6;12
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 The highest Common Devidor is 12.
 <br />
 <br />
 Methode 2:
 <br />
 <br />
</p>
<table border="1" width="100%">
 <tbody>
  <tr>
   <td width="20%" valign="top">
    Number1
    <br />
   </td>
   <td width="20%" valign="top">
    Number2
    <br />
   </td>
   <td width="20%" valign="top">
    Number3
    <br />
   </td>
   <td width="20%" valign="top">
    Number4
    <br />
   </td>
   <td width="20%" valign="top">
    Common Devisors
    <br />
   </td>
  </tr>
  <tr>
   <td width="20%" valign="top">
    24
    <br />
   </td>
   <td width="20%" valign="top">
    36
    <br />
   </td>
   <td width="20%" valign="top">
    60
    <br />
   </td>
   <td width="20%" valign="top">
    96
    <br />
   </td>
   <td width="20%" valign="top">
    2
    <br />
   </td>
  </tr>
  <tr>
   <td width="20%" valign="top">
    12
    <br />
   </td>
   <td width="20%" valign="top">
    18
    <br />
   </td>
   <td width="20%" valign="top">
    30
    <br />
   </td>
   <td width="20%" valign="top">
    48
    <br />
   </td>
   <td width="20%" valign="top">
    2
    <br />
   </td>
  </tr>
  <tr>
   <td width="20%" valign="top">
    6
    <br />
   </td>
   <td width="20%" valign="top">
    9
    <br />
   </td>
   <td width="20%" valign="top">
    15
    <br />
   </td>
   <td width="20%" valign="top">
    24
    <br />
   </td>
   <td width="20%" valign="top">
    3
    <br />
   </td>
  </tr>
  <tr>
   <td width="20%" valign="top">
    2
    <br />
   </td>
   <td width="20%" valign="top">
    3
    <br />
   </td>
   <td width="20%" valign="top">
    5
    <br />
   </td>
   <td width="20%" valign="top">
    6
    <br />
   </td>
   <td width="20%" valign="top">
    <br />
   </td>
  </tr>
 </tbody>
</table>
<p>
 <br />
 The Highest Common Devidor is: 2*2*3=12
 <br />
 <br />
 <span style="font-weight: bold;">
  Notes to create:
 </span>
 To find the HCD , first ffind the devisors of each numbe, list the commonn devisors and the take the highest(greatest ) or devide by lowest devisor continue to devide until when there is no common devisor other than one and mulltipply the divisors to find the HCD.
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 <br />
 <span style="font-weight: bold;">
  Notice:
 </span>
 A devisor or factor is a number which devids another.
 <br />
 <br />
 Example3: Find the multiples of 5 and of 11
 <br />
 <br />
 <span style="font-weight: bold;">
  SOLUTION:
 </span>
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 <br />
 a) The multiples of 5 are: 5;10;15;20;25;30;35;40;........
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 b) The multiplees of 11 are: 11;22;33;44;55;66;77;........
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 <br />
 <span style="font-weight: bold;">
  Notes to create:
 </span>
 The multiples of a number are obtained by multiplying that number by the countinng numbers by starting at one.
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 <br />
 Example4: Find the multiples of 20 less than 90
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 <br />
 <span style="font-weight: bold;">
  SOLUTION:
 </span>
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 <br />
 20*1; 20*2; 20*3; 20*4; 20*5
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 The multiples of 20 ={20; 40; 60; 80}
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 <br />
 Example5: Find the Lowest Common Multiples(LCM) of 6 and 9 less than 40.
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 a) Multiples of 6=6*1; 6*2; 6*3; 6*4; 6*5; 6*6={6; 12;18; 24; 36}
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 b) Multiples of 9=9*1; 9*2; 9*3; 9*4={9; 18; 36}
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 The common multiples of 6 and 9 are 18 and 36
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 Thus the Lowest Common Multiples of 6 and 9 is 18.
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 <br />
 Example 6: Find the LCM of tthis set of numbers.
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 12; 28 and 42.
 <br style="font-weight: bold;" />
 <br style="font-weight: bold;" />
 <span style="font-weight: bold;">
  SOLUTION:
 </span>
 <br />
 a) The multiples of 12=12*1; 12*2; 12*3; 12*4; 12*5; 12*6; 12*7; 12*88=
 <br />
 {12; 24; 36; 48; 60; 72;
 <span style="color: #ff0000;">
  84
 </span>
 ,........}
 <br />
 <br />
 b)) The multipples of 28=28*1; 28*2; 28*3 ; 28*4; 28*5; 28*6;.....=
 <br />
 {28; 46;
 <span style="color: #ff0000;">
  84
 </span>
 ;.......}
 <br />
 <br />
 c) The multiples of 42=42*1; 42*2; 42*3; 42*4;={42;
 <span style="color: #ff0000;">
  84
 </span>
 ; ........}
 <br />
 <br />
 The Lowest Common Multiples of 12;28 and 42 is 84
 <br />
 <br />
 <span style="font-weight: bold;">
  Notes to create:
 </span>
 To fid the Lowest Common Multiple, you list the common multiples and then you take the Lowest.
 <br />
 <br />
 Example 7: What are the prime numbers among the following and why.
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 1,4,2,7,9,27,17,107,108.
 <br style="font-weight: bold;" />
 <br style="font-weight: bold;" />
 <span style="font-weight: bold;">
  SOLUTION:
 </span>
 <br />
 The prime numbers are {1,2,7,17,107} because you can not find any number other than one and the number itself which can devide thay number.
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 <br />
 Example 8: Find the prime ffactors of 36 and write 36 as a product of prime factors.
 <br />
 <br style="font-weight: bold;" />
 <span style="font-weight: bold;">
  SOLUTION:
 </span>
 <br />
 <br />
</p>
<table border="1" width="100%">
 <tbody>
  <tr>
   <td width="50%" valign="top">
    Number
    <br />
   </td>
   <td width="50%" valign="top">
    Devisor
    <br />
   </td>
  </tr>
  <tr>
   <td width="50%" valign="top">
    36
    <br />
   </td>
   <td width="50%" valign="top">
    2
    <br />
   </td>
  </tr>
  <tr>
   <td width="50%" valign="top">
    18
    <br />
   </td>
   <td width="50%" valign="top">
    2
    <br />
   </td>
  </tr>
  <tr>
   <td width="50%" valign="top">
    9
    <br />
   </td>
   <td width="50%" valign="top">
    3
    <br />
   </td>
  </tr>
  <tr>
   <td width="50%" valign="top">
    3
    <br />
   </td>
   <td width="50%" valign="top">
    3
    <br />
   </td>
  </tr>
  <tr>
   <td style="vertical-align: top;">
    1
    <br />
   </td>
   <td style="vertical-align: top;">
    <br />
   </td>
  </tr>
 </tbody>
</table>
<p>
 <br />
 The prime factors of 36 are 2 and 3
 <br />
 therefore 36=2**2*3*3
 <br />
 36=2
 <sup>
  2
 </sup>
 *3
 <sup>
  2
 </sup>
 <sup>
 </sup>
 <sup>
  <br />
  <br />
 </sup>
 Notes to create: To find the prime factors of number, you devide tthat number using prime numbers only by starting at 2.
 <sup>
  <br />
  <br />
 </sup>
 The prime factors are presented as a product of prime fators or in power form.
 <sup>
  <br />
  <br />
 </sup>
</p>