Results 1 to 2 of 2

Math Help - factorial question

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    110

    factorial question

    determine how many zeros are at the end of the numerals for the following numbers.

    a. 10!

    b. 100!

    c. 1000!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, ihavvaquestion!

    Determine how many zeros are at the end of the numerals for the following numbers.

    . . (a)\;10!  \qquad (b)\;100! \qquad (c)\;1000!

    Every factor of 5 (combined with an even number) creates a final zero.

    The question becomes: How many factors-of-5 are contained in n! ?



    (a)\;10!

    We know that: . 10! \:=\:1\cdot2\cdot3\cdots 10
    And every 5th number contains a factor-of-5: . \left[\frac{10}{5}\right] \:=\:2 factors-of-5
    Therefore: . 10! ends in two zeros.



    (b)\;100!

    Every 5th number contains a factor-of-5: . \left[\frac{100}{5}\right] \:=\:20 factors-of-5.

    But every 25th number contains 5^2
    Each contributes an additional factor-of-5: . \left[\frac{100}{25}\right]\:=\:4 more factors-of-5.

    Therefore, 100! ends in: . 20 + 4 \:=\:24 zeros.



    (c)\;1000!

    Every fifth number contains a factor-of-5: . \left[\frac{1000}{5}\right] \:=\:200 factors-of-5.

    But every 25th number contains 5^2
    Each contributes another factor-of-5: . \left[\frac{1000}{25}\right] \:=\:40 more factors-of-5.

    And every 125th number contains 5^3
    Each contributes another factor-of-5: . \left[\frac{1000}{125}\right] \:=\:8 more factors-of-5.

    And every 625th number contains 5^4
    Each contributes yet another factor-of-5" . \left[\frac{1000}{625}\right] \:=\:1 more factor-of-5.


    Therefore, 1000! ends in: . 200 + 40 + 8 + 1 \:=\:249 zeros.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factorial question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 18th 2011, 04:08 PM
  2. 3x2 Factorial Design Question
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 4th 2010, 09:53 AM
  3. [SOLVED] Factorial series question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 30th 2009, 05:49 PM
  4. simple factorial question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 2nd 2008, 07:32 AM
  5. Replies: 6
    Last Post: September 12th 2007, 07:48 AM

Search Tags


/mathhelpforum @mathhelpforum