Results 1 to 2 of 2

Math Help - Number of trailing zero?

  1. #1
    Newbie
    Joined
    Aug 2012
    From
    manila
    Posts
    9

    Number of trailing zero?

    Find the number of trailing zeros in the ordinary decimal representation of the number:
    Number of trailing zero?-interval.jpg
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630

    Re: Number of trailing zero?

    Hello, musngiburger!

    Find the number of trailing zeros in the ordinary decimal representation of the number: . {123\choose45}

    We have: . {123\choose45} \:=\:\frac{123!}{45!\,78!}

    The numerator is: . 79\cdot80\cdot81\,\cdots\, 123

    The denominator is: . 1\cdot2\cdot3\,\cdots\,45

    The number of trailing zeros depends on the number of factors-of-5
    . . that remain in the numerator after reducing the fraction.


    The numbers in the numerator which have a factor-of-5 are:
    . . 80,85,90,95,100,105,110,115,120
    There are ten factors-of-5. .(100 has two.)

    The numbers in the denominator which have a factor of 5 are:
    . . 5,10,15,20,25,30,35,40,45
    There are ten factors-of-5. .(25 has two.)

    We find that all the factors-of-5 cancel out.

    Therefore, there are no trailing zeros in {123\choose45}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: January 16th 2012, 01:21 AM
  2. Replies: 4
    Last Post: April 28th 2011, 06:20 AM
  3. Replies: 2
    Last Post: August 19th 2010, 09:32 PM
  4. Replies: 2
    Last Post: December 18th 2008, 05:28 PM
  5. Replies: 5
    Last Post: October 7th 2008, 12:55 PM

Search Tags


/mathhelpforum @mathhelpforum