Results 1 to 6 of 6

Math Help - ABC is a 3-digit number such that its digits A, B and C form an arithmetic sequence..

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    15

    ABC is a 3-digit number such that its digits A, B and C form an arithmetic sequence..

    Let ABC be a 3-digit number such that its digits A, B, and C form and arithmetic sequence. The largest integer that divides all numbers of form ABCABC is.....?


    please give me the complete solution of this problem.....
    Last edited by jpmath2010; November 30th 2010 at 04:28 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,861
    Thanks
    742
    Hello, jpmath2010!

    Is that the exact wording of the problem?
    As stated. it's a silly problem . . .


    \text{Let }ABC\text{ be a 3-digit number such that its digits }A, B, C
    . . . \text{form an arithmetic sequence.}
    \text{The largest integer that divides all numbers of form }ABC\!ABC\text{ is ... ?}

    The largest integer that divides ABC\!ABC is . . . ABC\!ABC.

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2010
    From
    NJ
    Posts
    68
    3003.

    Soroban, he is asking what number divides ALL numbers of this form. For example,
    the GCD of 123123 and 135135 is 3003. The GCD of 147147 and 963963 is also 3003.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2010
    Posts
    15

    Smile

    thank you soroban for your effort....Any way the problem i have posted is come the Mathematics Olympiad.That is the exact problem. would you please give me the exact solution of that problem.
    Last edited by jpmath2010; November 30th 2010 at 04:52 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,861
    Thanks
    742
    Hello, jpmath2010!

    Now I get it . . .


    Let ABC be a 3-digit number such that its digits form and arithmetic sequence.
    Find the largest integer that divides all numbers of form ABC\!ABC

    Let \,h = hundreds digit of the three-digit number,
    . . and \,d be the common difference of the arithmetic sequence.

    Then: . ABC \;=\;100h + 10(h+d) + h+2d \:=\:111h + 3d \:=\:3(37h + d)


    Hence: . ABC\!ABC \;=\;1001\cdot ABC \;=\;1001\cdot 3(37h + d) \;=\;3003(37h + d)


    Therefore, the largest divisor is 3003.

    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2010
    Posts
    15
    wow thats great....i really thank you so much....have a nice day and God bless...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number of 4 digit codes in logarithmic form.
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 7th 2011, 08:14 AM
  2. Replies: 5
    Last Post: March 3rd 2011, 04:06 AM
  3. Number of Terms in an Arithmetic Sequence
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 17th 2009, 06:28 AM
  4. Replies: 2
    Last Post: December 26th 2008, 11:13 AM
  5. Sum of the digits of a two-digit number is ten..
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 10th 2007, 04:54 PM

Search Tags


/mathhelpforum @mathhelpforum