Results 1 to 3 of 3

Math Help - Find the last six digits of...

  1. #1
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Find the last six digits of...

    Let n be a positive integer with all digits equal to 5 such that n is divisible by 2003. Find the last six digits of \frac{n}{2003}.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2008
    Posts
    2
    55555555555555

    And I dont even know how you could use a formula... ah well.. trial and error does work sometimes.

    Last six digits are 173518 as total resulting number is
    27736173518

    Bearing in mind you needed 6 digits at least, so number would need 9(?) 5's at least.

    I just used trial and error....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    49
    Quote Originally Posted by alexmahone View Post
    Let n be a positive integer with all digits equal to 5 such that n is divisible by 2003. Find the last six digits of \frac{n}{2003}.
    Hello

    Here is one way, I think.

    If you are familiar with Napier's Bones method of multiplication then you can work 'backwards' to find the digits.

    The last digit of \frac{n}{2003} must be 5, since that is the only digit, (0 to 9), that will give you a number ending in 5 when multiplied by 3. The next digit must be 8, the only digit that will give you a number ending in 4, when multiplied by 3.

    Please see the attachment below.

    Can you see how to get the rest of the digits you need?

    Hope that helps.
    Attached Thumbnails Attached Thumbnails Find the last six digits of...-finding-last-six-digits.bmp  
    Last edited by Ting; October 17th 2008 at 07:38 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find the last two digits
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 25th 2011, 09:26 AM
  2. Replies: 0
    Last Post: January 16th 2011, 02:49 PM
  3. Replies: 7
    Last Post: November 28th 2010, 10:22 PM
  4. Find sum of the digits of B?
    Posted in the Number Theory Forum
    Replies: 10
    Last Post: August 15th 2008, 09:04 PM
  5. Replies: 2
    Last Post: April 3rd 2007, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum