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Help needed: calculating a grid layout for a given number...?

  • 04-11-2018 7:25pm
    #1
    Dinarius
    Registered Users Posts: 3,393 ✭✭✭


    Is there a way of working out if a given number can be can be expressed as a grid?

    E.g. 100 can be expressed as 10 x 10, 5 x 20, 2 x 50, whatever...

    So, if I have a much larger number, is there a way of seeing if it can be expressed as a grid, without any gaps, if you see what I mean?

    E.g. 2578, 2738, whatever...

    Thanks.

    D.


Comments

  • #2
    amcalester
    Closed Accounts Posts: 4,121 ✭✭✭amcalester


    Would all numbers not be gridable? Even prime numbers could be 1 x N where N is the prime number.

    Conversely all numbers bar prime numbers have more than 1 grid option.


  • #3
    Dinarius
    Registered Users Posts: 3,393 ✭✭✭Dinarius


    amcalester wrote: »
    Would all numbers not be gridable? Even prime numbers could be 1 x N where N is the prime number.

    Conversely all numbers bar prime numbers have more than 1 grid option.

    Thanks.

    So, let’s say 2738. Is that a prime number? Can it be expressed in any grid formation?

    Thanks.

    D.


  • #4
    amcalester
    Closed Accounts Posts: 4,121 ✭✭✭amcalester


    Dinarius wrote: »
    Thanks.

    So, let’s say 2738. Is that a prime number? Can it be expressed in any grid formation?

    Thanks.

    D.

    2738 is an even number so isn’t a prime, it can be

    2 x 1369
    37 x 74

    And then the opposite

    1369 x 2
    74 x 37

    You just want the factors of the number in question and those are your grids.


  • #5
    Dinarius
    Registered Users Posts: 3,393 ✭✭✭Dinarius


    amcalester wrote: »
    2738 is an even number so isn’t a prime, it can be

    2 x 1369
    37 x 74

    And then the opposite

    1369 x 2
    74 x 37

    You just want the factors of the number in question and those are your grids.

    Brilliant!

    So, apart from 74 x 37, what other grid options do I have?

    Really grateful for this.

    Thanks!

    D.

    Ps. 2 x 1369 is way to elongated. 74 x 37 is much closer to the kind of rectangle I want.


  • #6
    amcalester
    Closed Accounts Posts: 4,121 ✭✭✭amcalester


    Dinarius wrote: »
    Brilliant!

    So, apart from 74 x 37, what other grid options do I have?

    Really grateful for this.

    Thanks!

    D.

    Ps. 2 x 1369 is way to elongated. 74 x 37 is much closer to the kind of rectangle I want.


    For 2738? None, those are the only factors. No other combination of 2 whole numbers can be multiplied to give you 2738.


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  • #7
    Dinarius
    Registered Users Posts: 3,393 ✭✭✭Dinarius


    That sorts it.

    Many thanks!

    D.


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