Computer Shopper 125/Computer Shopper CD-ROM Issue 125 (1998-07)(Dennis Publishing).iso/EuroMath/MathDemo/DataBase/Question/ID451.txt

Text File | 1997-01-09 | 10.5 KB | 497 lines

*'<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>
'>/\<
'<\/>          n0105 - Question B
'>/\<
'<\/>          Highest Common Factor
'>/\<
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@WeightingScore 9,2,1,1

@atGraphic 32,14
@Picture numbers\n0105a.bmp

@at 106,24
Find the #bhighest common #
#bfactor# of the following
numbers:
@at 10,+8
                   #^  #p24#         #^  #p32#         #^  #p40#

@at 10,+62
      Which method do you want to practise?
@at ,+6
      Listing the #bfactors# of each number...
@at ,+4
      Using #bprime numbers#...

@MultMode 2
@atGraphic 214,164
@Loop 2
@HSPicture uncheck.bmp,check.bmp
@atGraphic ,180
@EndLoop

@Answer 0,2
@Feedback 0
@FBMGoto Method_2
@Answer 0,1

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@Question

@at 10,+32
What's the first step?
@at ,+3
#[K]

@keyPointAnswer 1,10,find all the factors of each number

@KeyPointFeedback 0,Wrong option
The first step will be to find all the
factors of each number.


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@Question

@NewPage
@atGraphic 32,14
@Picture numbers\n0105a.bmp

@at 106,24
Find the #bhighest common #
#bfactor# of the following
numbers:

@at 10,+8
                   #^  #p24#         #^  #p32#         #^  #p40#
@at ,+2
#T ;
@MarkPos 1
#T#T ;
@MarkPos 2
#T#T#T ;
@MarkPos 3

@InputWidth 20
@GoPos 1
@Loop 8
#[N]
@at ,+5
@EndLoop

@at 20,+4
Enter the factors from lowest to highest.
@MarkPos 4

@Answer 2, 1,2,3,4,6,8,12,24

@Feedback 1, 24,12,8,6,4,3,2,1
Your answers are correct, but you've given
them in reverse order. You must read questions
carefully.
@FBMGoto Next

@Feedback E0.25,?,?,?,?,?,?,?,?
That's partly right.*
@Feedback 0,?,?,?,?,?,?,?,?
The factors of a number are the whole numbers
which can divide that number and leave no remainder.
When you divide and there is no remainder, the number
you divided by, and the result of the division are both factors:*

@FeedbackC   1,Every number can be divided by 1, so #b1# is always a factor.
@FeedbackC 2|7,24 ≈ 2 = 12...  #b2# and #b12# are factors.
@FeedbackC 3|6,24 ≈ 3 = 8...    #b3# and #b8# are factors.
@FeedbackC 4|5,24 ≈ 4 = 6...    #b4# and #b6# are factors.
@FeedbackC 8,Every number can be divided by itself, so #b24# is also a factor.*
@FeedbackC 4|5,24 ≈ 5 = 4.8...     This does not divide evenly, so 5 is not a factor.
@FeedbackC 5|6,24 ≈ 7 = 3.429... 7 does not divide evenly, so it is not a factor either.

@Label Next

'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/

@Question

@GoPos 2
@Loop 6
#[N]
@at ,+5
@EndLoop

@Answer 2, 1,2,4,8,16,32

@Feedback 1, 32,16,8,4,2,1
Your answers are correct, but you've given
them in reverse order. You must always read
questions carefully.
@FBMGoto Next

@Feedback E0.3,?,?,?,?,?,?
That's partly right.*
@Feedback 0,?,?,?,?,?,?
The factors of a number are the whole numbers
which can divide that number and leave no remainder.
When you divide and there is no remainder, the number
you divided by, and the result of the division are both factors:*

@FeedbackC   1,Every number can be divided by 1, so #b1# is always a factor.
@FeedbackC 2|5,32 ≈ 2 = 16...  #b2# and #b16# are factors.
@FeedbackC 3|4,32 ≈ 4 = 8...    #b4# and #b8# are factors.
@FeedbackC 6,Every number can be divided by itself, so #b32# is also a factor.*
@FeedbackC 4|5,32 ≈ 3 = 10.6...     This does not divide evenly, so 3 is not a factor.
@FeedbackC 5|6,32 ≈ 5 = 6.4...       5 does not divide evenly, so it is not a factor either.

@Label Next


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@Question

@GoPos 3
@Loop 8
#[N]
@at ,+5
@EndLoop

@Answer 2, 1,2,4,5,8,10,20,40

@Feedback 1, 40,20,10,8,5,4,2,1
Your answers are correct, but you've given
them in reverse order. You must read questions
carefully.
@FBMGoto Next

@Feedback E0.25,?,?,?,?,?,?,?,?
That's partly right.*
@Feedback 0,?,?,?,?,?,?,?,?
The factors of a number are the whole numbers
which can divide that number and leave no remainder.
When you divide and there is no remainder, the number
you divided by, and the result of the division are both factors:*

@FeedbackC   1,Every number can be divided by 1, so #b1# is always a factor.
@FeedbackC 2|7,40 ≈ 2 = 20...  #b2# and #b20# are factors.
@FeedbackC 3|6,40 ≈ 4 = 10...  #b4# and #b10# are factors.
@FeedbackC 4|5,40 ≈ 5 = 8...    #b5# and #b8# are factors.
@FeedbackC 8,Every number can be divided by itself, so #b40# is also a factor.*
@FeedbackC 4|5,40 ≈ 3 = 13.333...   This does not divide evenly, so 3 is not a factor.
@FeedbackC 5|6,40 ≈ 6 = 6.666...     6 does not divide evenly, so it is not a factor either.

@Label Next


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@Question

@GoPos 4
@at 10,+6
Now what do you do?
@at ,+3
#[K]

@keyPointAnswer 1,9,find highest number in all the lists

@KeyPointFeedback 0,Wrong option
The final step is to find the highest factor that
is common to all three numbers.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/


@Question

@InputWidth 24

@at 100,+7
#b      Highest#
#bCommon Factor#
@at ,+3
           #[N]

@Answer 1, 8

@Feedback 0,?
You should have found the highest number in
all the lists.  #b8# is the highest factor common
to all three numbers.

@Feedback 1
That's right!  Well done.

@Goto End_of_Question



'<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>     METHOD 2    <\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>



@Label Method_2

@Question

@at 10,+32
What's the first step?
@at ,+3
#[K]

@keyPointAnswer 1,187,find the prime factors of each number

@KeyPointFeedback 0,Wrong option
The first step will be to find all the
prime factors of each number.


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@NewPage
@atGraphic 32,14
@Picture numbers\n0105a.bmp

@at 106,24
Find the #bhighest common #
#bfactor# of the following
numbers:
@at 10,+8
   #^          #p24#         #^          #p32#         #^          #p40#;
#T ;
@MarkPos 1
#T#T ;
@MarkPos 2
#T#T#T ;
@MarkPos 3

@InputWidth 20
@GoPos 1
#^        #^;
@Loop 5
#T#[N];
@at ,+17
#T#T#[N];
@EndLoop

@Answer 1.5, 2,12,2,6,2,3,3,1,,

@Feedback E0.15,?,?,?,?,?,?,?,?,?,?
@Feedback 0,?,?,?,?,?,?,?,?,?,?

@FeedbackC 0,To find all the prime factors of any number,
@FeedbackC 0,first divide by the smallest prime number as
@FeedbackC 0,many times as possible.  If the number will
@FeedbackC 0,not divide evenly, divide by the next larger
@FeedbackC 0,prime number, and repeat until you are left
@FeedbackC 0,with a result of 1.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/


@Label Next
@Question

@GoPos 1
@at 20,+110
The Prime Factors are...

@InputWidth 14
@GoPos 1
@at -16,+140
#[N];
@at ,-10
#[N];
@at ,+10
 ╫ #[N];
@at ,-10
#[N]

@Answer 0.5, 2,3,3,
@Feedback 0.5
@FBMGoto Next
@Answer 0.5, 3,1,2,3
@Feedback 0.5
@FBMGoto Next
@Answer 0.5, 2,3,3,1
@Feedback E0.125,?,?,?,?
@Feedback 0,?,?,?,?

@FeedbackC 0,Once you've worked out all the prime factors,
@FeedbackC 0,you should rewrite each factor once, raising
@FeedbackC 0,it to an index to show how many lots there
@FeedbackC 0,are.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/

@Label Next
@Question

@InputWidth 20
@GoPos 2
#^        #^;
@Loop 5
#T#[N];
@at ,+17
#T#T#[N];
@EndLoop

@Answer 1.5, 2,16,2,8,2,4,2,2,2,1

@Feedback E0.15,?,?,?,?,?,?,?,?,?,?
@Feedback 0,?,?,?,?,?,?,?,?,?,?

@FeedbackC 0,To find all the prime factors of any number,
@FeedbackC 0,first divide by the smallest prime number as
@FeedbackC 0,many times as possible.  If the number will
@FeedbackC 0,not divide evenly, divide by the next larger
@FeedbackC 0,prime number, and repeat until you are left
@FeedbackC 0,with a result of 1.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/


@Label Next
@Question

@InputWidth 14
@GoPos 2
@at +10,+140
#[N];
@at ,-10
#[N]

@Answer 0.5, 2,5

@Feedback E0.25,?,?
@Feedback 0,?,?

@FeedbackC 0,Once you've worked out all the prime factors,
@FeedbackC 0,you should rewrite each factor once, raising
@FeedbackC 0,it to an index to show how many lots there
@FeedbackC 0,are.

'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/


@Label Next
@Question

@InputWidth 20
@GoPos 3
#^        #^;
@Loop 5
#T#[N];
@at ,+17
#T#T#[N];
@EndLoop

@Answer 1.5, 2,20,2,10,2,5,5,1,,

@Feedback E0.15,?,?,?,?,?,?,?,?,?,?
@Feedback 0,?,?,?,?,?,?,?,?,?,?

@FeedbackC 0,To find all the prime factors of any number,
@FeedbackC 0,first divide by the smallest prime number as
@FeedbackC 0,many times as possible.  If the number will
@FeedbackC 0,not divide evenly, divide by the next larger
@FeedbackC 0,prime number, and repeat until you are left
@FeedbackC 0,with a result of 1.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/


@Label Next
@Question

@InputWidth 14
@GoPos 3

@at -5,+140
#[N];
@at ,-10
#[N];
@at ,+10
 ╫ #[N];
@at ,-10
#[N]

@Answer 0.5, 5,1,2,3
@feedback 0.5
@fbmGoto next
@Answer 0.5, 2,3,5,1

@Feedback E0.125,?,?,?,?
@Feedback 0,?,?,?,?

@FeedbackC 0,Once you've worked out all the prime factors,
@FeedbackC 0,you should rewrite each factor once, raising
@FeedbackC 0,it to an index to show how many lots there
@FeedbackC 0,are.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/
@label next
@Question

@at 10,280
Now what do you do?
@at ,+3
#[K]

@keyPointAnswer 1,188,find the product

@KeyPointFeedback 0,Wrong option
The final step is to find the product of the
highest prime factor to the highest power
common to all three numbers.


'/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/

@Question

@InputWidth 14
@at 10,240
Highest Common Factor  =  #[N];
@at ,-10
#[N];
@at ,+10
  =  #[N]

@Answer 1, 2,3,8

@Feedback 0.5, 2,3,?
@FBMGoto Calc

@Feedback 0,?,?,?
To find the highest common factor of a given
number, you take only the prime factors which
are in all of the lists, in this case 2. If the prime factors
are raised to an index, you should take the lowest.
In this case the highest common power of 2 is 3._
@Label Calc
The highest common factor of 24, 32 and 40 is:*
                  #b2ë = 8#

@Feedback 1
That's right!  Well done.


'<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>/\<\/>


@Label End_of_Question