Results 1 to 4 of 4
Like Tree2Thanks
  • 2 Post By HallsofIvy

Math Help - 8 digit number

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    US
    Posts
    37
    Thanks
    1

    8 digit number

    Find a 8 digit number which starts with 1984 and is divisible by 6,7,8,9.Step by step explanation will be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,393
    Thanks
    1327

    Re: 8 digit number

    So the number is . Any number divisible by both 8 and 9 is necessarily divisble by 6 so we really only need to check "divisible by 8", divisible by 7" and "divisible by 9".

    To be divisible by 8, the first three digits must make a number divisible by : 008, 016, 024, 032, 040, 048, etc.

    To be divisible by 9, the sum of the digits must be divisible by 9: 1+9+ 8+ 4= 22 so 22+ a+ b+ c+ d must be divisible by 9.
    22+ 0+ 0+ 8= 30
    22+ 0+ 1+ 6= 29
    22+ 0+ 2+ 4= 28
    22+ 0+ 3+ 2= 27 is divisible by 9 so 1984a032 is a candidat
    22+ 0+ 4+ 0= 26
    22+ 0+ 4+ 8= 34
    22+ 0+ 5+ 6= 33
    22+ 0+ 6+ 4= 32
    22+ 0+ 7+ 2= 31
    22+ 0+ 8+ 0= 30
    22+ 0+ 8+ 8= 38
    22+ 0+ 9+ 6= 37
    22+ 1+ 0+ 4= 27 so 1984a104 is a candidate, etc.

    A number is divisible by 7 if and only if after taking the last digit off the number, doubling that last digit and subtracting from the truncated number, the result is divisible by 7. For example 805 is divisible by 7 because we drop the last digit, 5, we have 80. Subtracting 2(5)= 10 from that gives 70 which is obviously divisible by 7.
    Thanks from RuyHayabusa and topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2013
    From
    Austin
    Posts
    5

    Re: 8 digit number

    I multiplied 6*7*8*9 together to get 3024.

    I know that i can multiply any number by 3024 and it will be divisible by 6, 7, 8, or 9.

    then by trial and error (2 mintues) i zeroed in on a number to multiply 3024 by to get the required number. 3024 * 6563 to get 19846512.
    Last edited by zendo; February 21st 2013 at 07:13 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2013
    From
    US
    Posts
    37
    Thanks
    1

    Re: 8 digit number

    Quote Originally Posted by HallsofIvy View Post
    So the number is . Any number divisible by both 8 and 9 is necessarily divisble by 6 so we really only need to check "divisible by 8", divisible by 7" and "divisible by 9".

    To be divisible by 8, the first three digits must make a number divisible by : 008, 016, 024, 032, 040, 048, etc.

    To be divisible by 9, the sum of the digits must be divisible by 9: 1+9+ 8+ 4= 22 so 22+ a+ b+ c+ d must be divisible by 9.
    22+ 0+ 0+ 8= 30
    22+ 0+ 1+ 6= 29
    22+ 0+ 2+ 4= 28
    22+ 0+ 3+ 2= 27 is divisible by 9 so 1984a032 is a candidat
    22+ 0+ 4+ 0= 26
    22+ 0+ 4+ 8= 34
    22+ 0+ 5+ 6= 33
    22+ 0+ 6+ 4= 32
    22+ 0+ 7+ 2= 31
    22+ 0+ 8+ 0= 30
    22+ 0+ 8+ 8= 38
    22+ 0+ 9+ 6= 37
    22+ 1+ 0+ 4= 27 so 1984a104 is a candidate, etc.

    A number is divisible by 7 if and only if after taking the last digit off the number, doubling that last digit and subtracting from the truncated number, the result is divisible by 7. For example 805 is divisible by 7 because we drop the last digit, 5, we have 80. Subtracting 2(5)= 10 from that gives 70 which is obviously divisible by 7.
    Thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Digit sum & digit product of number x
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 19th 2011, 08:07 AM
  2. 4 digit PIN number - please help
    Posted in the Statistics Forum
    Replies: 4
    Last Post: February 12th 2010, 05:47 AM
  3. 10 digit number
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: November 2nd 2009, 01:51 PM
  4. two-digit number
    Posted in the Algebra Forum
    Replies: 6
    Last Post: October 10th 2009, 07:59 AM
  5. Let N be a 5 digit number...
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: March 1st 2007, 01:29 PM

Search Tags


/mathhelpforum @mathhelpforum