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Division Algorithm

  1. Feb 24, 2004 #1
    If I have to find the quotient q and the remainder r and:

    a = -5286
    b = 19

    How do I go about writing down the steps for this algorithm? I know what the answer will be, but I need to be able to use the division algorithm to prove my answer. Like I know if:

    b > 0 and a < 0 (which in this case is true),

    then since -a > 0, a = (-q)b - r (where 0 <= r < b).

    But how would I know that q is equal to -279 and that the remainder is 15? (Pretending that I didn't the know answer already.)

  2. jcsd
  3. Feb 27, 2004 #2


    User Avatar
    Science Advisor

    I have absolutely no idea how you would "know that q is equal to
    -279 and that the remainder is 15" since -(-279)(19)-15 is NOT
    -5286 (nor is (-279)(19)-15). You have your signs mixed up.

    Did you try actually dividing? That is, after all what the division algorithm is!
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