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

Dinarius

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.

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.

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.

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.

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.

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.

Dinarius

That sorts it.

Many thanks!

D.