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Math Help - fenders -- srsli difficult

  1. #1
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    fenders -- srsli difficult

    hey guys

    could u guys hav a read of this q? coz its a monster one!!! so hard... siigh
    neway dis is da q..

    an eg:
    choose a number:156
    its factors are: 1,2,3,4,6,12,13,26,39,52,78,156
    grouped by last digit:{1}, {2,12,52}, {3,13}, {4}, {6,26,156}, {78}, {39}

    We say the fenders (factor enders) of 156 are 1,2,3,4,6,8,9 and that 156 is a 7-fender (meaning dat it had seven fenders)

    a) find a 1-fender which is composite
    b) Show that a number which has a 0 and a 9 as fenders has at least four more fenders
    c) the smallest 10 fender is less thaan 700. Find it and explain why is is the smallest

    Another 7-fender is 460--its set of fenders is (0,1,2,3,4,5,6,); which is different from the set of fenders of 156
    d) find three 9-fenders less than 1000 with different sets of fenders

    yea...its reeli hard... i hardly evn understand the q....
    plz try dis q!!
    any help would be like a call from heaven!!! lol :P
    thanx soooo much guys
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by phatjigga
    hey guys

    could u guys hav a read of this q? coz its a monster one!!! so hard... siigh
    neway dis is da q..

    an eg:
    choose a number:156
    its factors are: 1,2,3,4,6,12,13,26,39,52,78,156
    grouped by last digit:{1}, {2,12,52}, {3,13}, {4}, {6,26,156}, {78}, {39}

    We say the fenders (factor enders) of 156 are 1,2,3,4,6,8,9 and that 156 is a 7-fender (meaning dat it had seven fenders)

    a) find a 1-fender which is composite
    As 1 is a factor of every number, every factor of of a 1-fender must end in a
    1. Now if p is a prime ending in a 1, then p is a 1-fender, but not composite
    (composite means it has more factors that 1 and itself).

    Let p be a prime ending in a 1, what is the last digit of p^2? What are the
    factors of p^2 (which is composite)?

    RonL

    RonL
    Last edited by CaptainBlack; June 25th 2006 at 12:41 AM.
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  3. #3
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    thanx now i understand (a) but can anyone help me with the other ones?

    hey could neone be able to help me with b,c or d??
    thanx captain black 4 helping me with a.
    i stilll dont understand the other qs
    any help would be wonderful
    thanks guys
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by phatjigga
    hey guys

    could u guys hav a read of this q? coz its a monster one!!! so hard... siigh
    neway dis is da q..

    an eg:
    choose a number:156
    its factors are: 1,2,3,4,6,12,13,26,39,52,78,156
    grouped by last digit:{1}, {2,12,52}, {3,13}, {4}, {6,26,156}, {78}, {39}

    We say the fenders (factor enders) of 156 are 1,2,3,4,6,8,9 and that 156 is a 7-fender (meaning dat it had seven fenders)

    b) Show that a number which has a 0 and a 9 as fenders has at least four more fenders
    A number with 0 as a fender is divisible by 10, and so is divisible by all of
    the factors of 10, and hence has as fenders the last digits of all of the
    factors of 10 (2 is a factor of 10 and hence one of the fenders of any
    number with 0 as a fender). (since all the factors of 10 have a single digit
    they are in fact fenders)

    A number with a fender of 9 has a factor xwith last digit 9, and as 2 is a
    factor of our number with fenders 0 and 9, so is 2x. What is the fender of 2x?

    RonL

    Having got this far how many new fenders have you found?
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  5. #5
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    umm..

    Quote Originally Posted by CaptainBlack
    A number with 0 as a fender is divisible by 10, and so is divisible by all of
    the factors of 10, and hence has as fenders the last digits of all of the
    factors of 10 (2 is a factor of 10 and hence one of the fenders of any
    number with 0 as a fender). (since all the factors of 10 have a single digit
    they are in fact fenders)

    A number with a fender of 9 has a factor xwith last digit 9, and as 2 is a
    factor of our number with fenders 0 and 9, so is 2x. What is the fender of 2x?

    RonL

    Having got this far how many new fenders have you found?

    to be truly honest, i hav absolutely no idea captain black
    i understand (a) quite well but then (b) .... im totally confused
    sorry....
    if it wouldnt be too much of a bother, could you please explain it to me again??
    thank you sooo much
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by phatjigga
    to be truly honest, i hav absolutely no idea captain black
    i understand (a) quite well but then (b) .... im totally confused
    sorry....
    if it wouldnt be too much of a bother, could you please explain it to me again??
    thank you sooo much
    The only way a number can have 0 as a fender is if it has a factor ending
    in a 0. A number ending in a 0 is divisible by 10, like 10, 20 ,30, ..

    But if a number is divisible by 10, it is divisible by all the proper divisors of 10
    which are 1, 2 and 5

    These divisors all have 1-digit, and so are fenders of the original number.

    Thus we already have three new fenders of our original number.

    If the original number has 9 as a fender it has a factor with last
    digit 9, call this x, now as 2 is also a factor of our original
    number so is 2x.

    What is the last digit of 2x? It is a fender of the original number,
    but is it different from the fenders we already have found?

    RonL
    Last edited by CaptainBlack; June 2nd 2006 at 10:41 PM.
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  7. #7
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    where is my question????
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  8. #8
    Grand Panjandrum
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    Talking

    Quote Originally Posted by Joyce
    where is my question????
    It is deleted. I have told you already not to tag questions onto the
    end of existing threads, but to create new threads (in an appropriate
    forum -urgent homework, or trigonometry would seem to be appropriate) for
    new questions.

    To create a new thread open a forum. There will be a button near the
    top on the left labelled "new thread", hit that and you will be able to
    create a new thread for your question.

    RonL
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