Question 1010060

an area {{{114in}}} high by {{{144in}}} wide:

{{{A=114in*144in}}}

{{{A=16416in^2}}}

 to know the largest tile you can use without having to cut the tile, find greatest common factor of {{{114}}} and {{{144}}}

{{{114= 2*3*19}}}  ({{{3}}} distinct prime factors) 
and {{{144=2^4*3^2}}}  ({{{6}}} prime factors, {{{2}}} distinct)

so, {{{gcf(114,144)=2*3=6}}}

and the largest tile will be {{{6in}}} by {{{6in}}}=>{{{36in^2}}}


{{{16416in^2/36in^2=456}}} tiles