Question 843511
As long as we do not need to be realistic, there is no maximum number of tiles.
In math-land my tiles could measure 1 nanometer by 1 nanometer, and I would use a huge number of those tiles.
 
There is a minimum number of tiles, corresponding to a maximum tile size, if I am not allowed to cut the tiles into pieces.
 
To line up a whole number of tiles along the 2016 cm length of the courtyard, I need square tiles with a side length that will go evenly into 2016 cm.
To line up a whole number of tiles along the 1560 cm width of the courtyard, I need square tiles with a side length that will go evenly into 1560 cm.
The tile side length on cm needs to be a factor of 2016 and 1560.
The maximum tile size corresponds to the greatest common factor of 2016 and 1560.
{{{2016=2^5*3^3*7}}}
{{{1560=2^3*3*5*13}}}
The greatest common factor is
{{{2^3*3=8*3=24}}}
The maximum tile size is {{{highlight(24cm)}}} by {{{highlight(24cm)}}} .
We would line up
{{{2016/24=2^5*3^3*7/(2^3*3)=2^2*3*7=84}}} tiles along the length of the courtyard and
{{{1560/24=2^3*3*5*13/(2^3*3)=5*13=65}}} tiles along the width of the courtyard.
That mean that we would use {{{84*65=2^2*3*5*7*13=20*39=5460}}} tiles.
We can also calculate that the surface area of the 24-cm tiles is
{{{(24cm)(24cm)=576cm^2}}}
while the surface area of the courtyard is
{{{(2016cm)(1560cm)=3144960cm^2}}}
and that it would take
{{{3144960cm^2/(576cm^2)=5460}}} times the surface area of one tilew to cover the whole courtyard.