Computer Shopper 125/Computer Shopper CD-ROM Issue 125 (1998-07)(Dennis Publishing).iso/EuroMath/MathDemo/DataBase/learning/ID154.txt

Text File | 1997-11-03 | 6.6 KB | 487 lines

¬@seeAlso 1factors
@seeAlso 1prime factors
@seeAlso 1lowest common multiple
@seeAlso 1multiples




'*************************************NUMBERS***********************
'***************************************************************************
'*****************HIGHEST COMMON FACTOR*********************

@atGraphic 5,15
@Picture numbers\n0105a.bmp




@at  0,5
#<highest common factor#

@PlaySoundFile n010501.wav



@animate BabStand,babTapStick

@At 75,23

@Definition
The highest common factor of a
set of numbers is the number
with the highest value that divides
exactly into all of them.


@prompt
@at 10,75
@keyPoint 9999,check the smallest number


@PlaySoundFile n010502.wav







Find the highest common factor of 18, 27and 45.

@Wait 0.5
@At ,+5


Before you take the time to use the method, do
a quick mental check to see if the #Bsmallest#
#Bnumber# is a #Bfactor# of the other numbers.

@Wait 0.5
@At ,+5

               #^   18          #^   27           #^   45

@Wait 0.5
@At ,+5
#T≈ 18    #T≈ 18    #T≈ 18

@Wait 0.5
@At ,+5
#T     #B1#    #T  #B1.5#    #T  #B2.5#

@Wait 0.5
@At ,+5

@PlaySoundFile n010503.wav

If it #Bis# then the #Bsmallest number# is the
#Bhighest# #Bcommon factor#.

@Wait 0.5
@At ,+5

Here it is #bnot#, so then use the following method:



@prompt
@keyPoint 10,find all the factors of each number





#BKey Step One#

@PlaySoundFile n010504.wav

First, #K10,*find all the factors of each number#.
@Wait 0.5
@At 33,105
#B18#

@Wait 0.5
@At 16,120

1,;
@Wait 0.25
2,;
@Wait 0.25
3,;
@Wait 0.25
6,;
@Wait 0.25
9,;
@Wait 0.25
18
@Wait 0.25


@At 25,135
≈ #b2# = #b9#
@Wait 0.25
≈ #b3# = #b6#
@Wait 0.25
≈ 4 = 4.5
@Wait 0.25
≈ 5 = 3.6
@Wait 0.25
≈ #b6# = #b3#
@Wait 0.25
≈ #b9# = #b2#

@At 105,105
#B27#

@Wait 0.5
@At 93,120
1,;
@Wait 0.25
3,;
@Wait 0.25
9,;
@Wait 0.25
27;
@Wait 0.25


@At 90,135
≈ 2 = 13.5
@Wait 0.25
≈ #b3# = #b9#
@Wait 0.25
≈ 4 = 6.75
@Wait 0.25
≈ 5 = 5.4
@Wait 0.25
≈ 6 = 4.5
@Wait 0.25
≈ 7 = 3.857
@Wait 0.25
≈ 8 = 3.375
@Wait 0.25
≈ #b9# = #b3#


@At 178,105
#B45#


@Wait 0.5
@At 157,120

1,;
@Wait 0.25
3,;
@Wait 0.25
5,;
@Wait 0.25
9,;
@Wait 0.25
15,;
@Wait 0.25
45
@Wait 0.25


@At 165,135
≈ 2 = 22.5
@Wait 0.25
≈ #b3# = #b15#
@Wait 0.25
≈ 4 = 11.25
@Wait 0.25
≈ #b5# = #B9#
@Wait 0.25
≈ 6 = 7.5
@Wait 0.25
≈ 7 = 6.429
@Wait 0.25
≈ 8 = 5.625
@Wait 0.25
≈ #b9# = #b5#



@prompt
@keyPoint 9,find the highest number in all the lists



@PlaySoundFile n010505.wav


@animate BabPointUp,BabPointWave,babPointDown



#BKey Step Two#
Then, #K9,find the highest number in all the#
#K9,lists#.
@Wait 0.5
@At 33,117
#B18#
@At 105,117
#B27#
@At 178,117
#B45#


@Wait 0.5
@At 16,132

1,;
@Wait 0.25
2,;
@Wait 0.25
3,;
@Wait 0.25
6,;
@Wait 0.25
#B9#,;
@Wait 0.25
18
@Wait 0.25

@At 90,132
1,;
@Wait 0.25
3,    ;
@Wait 0.25
#B9#,;
@Wait 0.25
27;
@Wait 0.25
@At 157,132

1,;
@Wait 0.25
3,;
@Wait 0.25
5,;
@Wait 0.25
#B9#,;
@Wait 0.25
15,;
@Wait 0.25
45
@Wait 0.25


@PlaySoundFile n010506.wav

@At 10,+10
#B9# is the #Bhighest common factor# of 18,
27 and 45.


@Wait 0.25

@At 10,+10

Remember, it is possible that there will be #Bno#
#Bhighest common factor#.





@prompt
@keyPoint 9999,second method


@PlaySoundFile n010507.wav


@animate BabPointUp,BabPointWave,babPointDown

The previous method involves a lot of working
out.

@Wait 0.5
@At 10,+10


For simple numbers you can often use #Btrial#
#Band improvement# methods more quickly
and easily.

@Wait 0.5
@At 10,+10


There is another method that works well,
particularly for larger numbers:


@prompt
@keyPoint 187,find the prime factors of each number





@PlaySoundFile n010508.wav

@animate BabStand,BabStickDown,BabGetCalculator,BabCalculate



#bKey Step One#

First, #K187,find the prime factors of each#
#K187,number#.
@Wait 0.5
@At ,+15

          #^#B18#                    #^#B27#                    #^#B45#
@Wait 0.5
@At ,+5
#T =#T =#T =
@Wait 0.5
@At ,+5

     2 ╫ 3 ╫ 3          3 ╫ 3 ╫ 3          3 ╫ 3 ╫ 5
@Wait 0.5
@At ,+5
        #B2# ╫ #B3ê#          #T#T #B3ë#         #B3ê# ╫ #B5#







@prompt
@keyPoint 188,find the product



@PlaySoundFile n010509.wav


@animate BabCalculate,BabPutCalculator,BabStickUp,BabStand


#bKey Step Two#

To find the #Bhighest common factor#, take only
the prime factors in #Ball# the lists and #K188,find#
#K188,the product#
@Wait 0.5
@At ,+2

          #^#B18#                    #^#B27#                    #^#B45#
@Wait 0.5
@At ,+2
#T =#T =#T =
@Wait 0.5
@At ,+2

     2 ╫ 3 ╫ 3          3 ╫ 3 ╫ 3          3 ╫ 3 ╫ 5
@Wait 0.5
@At ,+2
        #B2# ╫ #B3ê#          #T#T #B3ë#         #B3ê# ╫ #B5#


Take only the factors that are in all the lists but
if they include powers, take the highest
common one:     #B3ê#
The #Bhighest common factor# = #B9#


@prompt
@keyPoint 9999,summary (part 1)

#bSummary#

@Wait 0.75
@At ,+10
To find the highest common factor of a set of
numbers:
@Wait 0.75
@At ,+10
   *   #^Before you use the method, do a quick
#Tmental  check to see if the #Bsmallest#
#T#Bnumber# is a #Bfactor# of the other numbers
@Wait 0.75
@At ,+10
   *   #TIf it is then the #Bsmallest number# is the
#T#Bhighest##Bcommon factor#.

@At 175,215
#b(continued)#


@prompt
@keyPoint 9999,summary (part 2)

#b(continued)#

@Wait 0.75
@At ,+10

If it is #Bnot# then use the method:
@Wait 0.75
@At ,+10
   *   #^#K10,*find all the factors of each number#
@Wait 0.75
@At ,+10
   *   #T#K9,find the highest number in all the#
#T#K9,lists#
@Wait 0.75
@At ,+10
   *    #Tit is possible that there will be #Bno highest#
#t#Bcommon factor#.

@At 175,215
#b(continued)#








@prompt
@keyPoint 9999,summary (part 3)

#b(continued)#
@Wait 0.75
@At ,+10

A faster but harder method for finding the
#bhighest common factor# is to:

@Wait 0.75
@At ,+10

   *   #^first, #K187,find the prime factors of#
#T#K187,each number#

@Wait 0.75
@At ,+10

   *   #Tthen, take only the #Bprime factors# in
#T#Ball# the lists and #K188,*find the product#

@Wait 0.75
@At ,+10


   *   #Tif the prime factors include #Bpowers#,
#Ttake the highest common one.

   #Bpowers#,
#Ttake the highest common one.

  5
'@At ,+5


   *   #TIf the prime factors include #Bpowers#,
#Ttake the highest common one.