Results 1 to 2 of 2

Math Help - Find the divisor...

  1. #1
    Junior Member Bartimaeus's Avatar
    Joined
    Jul 2006
    Posts
    36

    Arrow Find the divisor...

    I havn't found an easy way yet, appreciate any help/working/thoughts.
    Narrowed it down to be less than 100 and greater than 30 (I think...pretty sure) by sheer number crunching.
    Here's the problem...


    When 823519 is divided by a number which is bigger than 1, ther remainder is three times the remainder obtained by dividing 274658 by the same number. Find the divisor.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    By the division algorithm ( a=bq+r with q=\lfloor \frac{a}{b} \rfloor (Here \lfloor x \rfloor denotes the largest integer not greater than x)) we have

    274658=m\left(\lfloor\frac{274658}{m}\rfloor \right)+r

    So
    r = 274658-m \left(\lfloor\frac{274658}{m}\rfloor \right)

    823519 \equiv 3 \left(274658-m \lfloor\frac{274658}{m}\rfloor \right)\mod m
     \Rightarrow m|823974-3m\left(\lfloor \frac{274658}{m} \rfloor\right) - 823519
    \Rightarrow m|455 \times 1 - 3m\left(\lfloor \frac{274658}{m} \rfloor \right)

    And because of the divisibility property: If a|b and a|c then (\forall m,n \in \Re) \ a|bm+cn

    So m divides one of 455 or 1. But since another property states that if a|b \Rightarrow b \geq a, and since it is a requirement that m \neq 1, we must have m|455

    Then m is a factor of 455

    The factors of 455 are: 1, 455, 5, 91, 7, 65, 13, 35

    By trial I get m = 91
    Last edited by DivideBy0; September 22nd 2007 at 04:13 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find all possible values of a divisor
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: September 15th 2011, 05:46 PM
  2. b is a Zero Divisor ( I think)
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: July 23rd 2011, 10:05 PM
  3. Find prime divisor
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: May 20th 2010, 10:04 AM
  4. divisor
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 17th 2009, 05:43 AM
  5. divisor
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: September 3rd 2007, 10:16 PM

Search Tags


/mathhelpforum @mathhelpforum