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Math Help - Need Urgent Help i'm unsure

  1. #1
    math_spartan
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    Need Urgent Help i'm unsure

    hey guys I need help with a problem concerning factors and a 3 digit number. I had the answer to this question as 891 using some algebra but my friend got a higher 3 digit number than me. Any help for the below question will be welcomed with open arms.

    Find the largest 3 digit number which has exactly 10 factors including 1 and itself.

    Yeah I have 891...is there a higher 3 digit number with 10 factors?

    Please help me!!

    ***

    i think i have the number i just need 2 know how to work it out so i can check
    Last edited by MathGuru; June 5th 2006 at 11:41 PM.
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by math_spartan
    hey guys I need help with a problem concerning factors and a 3 digit number. I had the answer to this question as 891 using some algebra but my friend got a higher 3 digit number than me. Any help for the below question will be welcomed with open arms.

    Find the largest 3 digit number which has exactly 10 factors including 1 and itself.

    Yeah I have 891...is there a higher 3 digit number with 10 factors?

    Please help me!!

    ***

    i think i have the number i just need 2 know how to work it out so i can check
    I think the number is 976
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  3. #3
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    me 2

    Quote Originally Posted by malaygoel
    I think the number is 976
    so do I...THe factors for 976 are 1 2 4 8 16 61 122 244 488 976. Hey malaygoel how did you work it out? I'm interested in different methods of working.
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  4. #4
    Super Member malaygoel's Avatar
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    Quote Originally Posted by mathemagician
    so do I...THe factors for 976 are 1 2 4 8 16 61 122 244 488 976. Hey malaygoel how did you work it out? I'm interested in different methods of working.
    Do you know how to find the no. of factors of a given number?
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  5. #5
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    no not really

    no not really...i used a factor calculator thing on the internet...can u tell me how to find the no. of factors for a given number...please?
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by math_spartan
    hey guys I need help with a problem concerning factors and a 3 digit number. I had the answer to this question as 891 using some algebra but my friend got a higher 3 digit number than me. Any help for the below question will be welcomed with open arms.

    Find the largest 3 digit number which has exactly 10 factors including 1 and itself.

    Yeah I have 891...is there a higher 3 digit number with 10 factors?

    Please help me!!

    ***

    i think i have the number i just need 2 know how to work it out so i can check
    Consider a number N with prime factorisation

    N=p_1^{n_1}p_2^{n_2}\dots p_m^{n_m},

    then the number of divisors of N is:

    d(N)=\prod_1^{m}(1+n_m).

    If d(N)=10, then either N is a ninth power of a single prime,
    or it a product of a prime and a fourth power of another prime (as 10 only
    has factorisations 1x10 and 2x5).

    If N<1000, in the first of these cases the only possible candidate for the
    prime is 2, and so then N=2^9=512.

    If N<1000, in the second of these cases the only possible candidates for the
    prime raised to the fourth power are 2,\ 3,\ 4. Then trial and
    error shows that the largest N<1000 that is a prime times the
    fourth power of one of these primes is:

    <br />
N=61\times 2^4=976<br />

    RonL
    Last edited by CaptainBlack; June 6th 2006 at 03:21 AM. Reason: Correction of typo spotted by EarBoth
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  7. #7
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    Quote Originally Posted by CaptainBlack
    ...
    <br />
N=91\times 2^4=976<br />

    RonL
    Hello,

    you calculated N=61\times 2^4=976, which fits better to your explanations.

    Greetings

    EB
    Last edited by CaptainBlack; June 6th 2006 at 02:59 AM.
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by earboth
    Hello,

    you calculated N=61\times 2^4=976, which fits better to your explanations.

    Greetings

    EB

    Opps..

    Must remember not to use that Escher note paper for scribbling down results
    in future

    RonL
    Attached Thumbnails Attached Thumbnails Need Urgent Help i'm unsure-escher-note.jpg  
    Last edited by CaptainBlack; June 6th 2006 at 04:24 AM.
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  9. #9
    Super Member
    earboth's Avatar
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    Quote Originally Posted by CaptainBlack
    Opps..
    Must remember not to use that Escher note paper for scribbling down results
    in future
    RonL
    Hello,

    if you are still using this kind of note paper you should better change your scribbling practice (see attachment).

    (By the way where did you know it from that Mijnheer M. C. Escher is one of my favourite artists? Or has the stealth group of this forum already scanned and cataloguized my personality, so there won't be any personality left?).

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Need Urgent Help i'm unsure-escher_handinhand.gif  
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  10. #10
    Grand Panjandrum
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    Quote Originally Posted by earboth
    Hello,

    if you are still using this kind of note paper you should better change your scribbling practice (see attachment).

    (By the way where did you know it from that Mijnheer M. C. Escher is one of my favourite artists? Or has the stealth group of this forum already scanned and cataloguized my personality, so there won't be any personality left?).

    Greetings

    EB
    I didn't know he was one of you favourite artist, it just so happens that
    I also admire his work.

    RonL
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