Square tiles

The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to cover the floor exactly.

Correct answer:

n =  105
a =  80 cm

Step-by-step explanation:

$$\begin{gathered} x=12\text{m}\to \text{cm}=12\cdot 100\text{cm}=1200\text{cm} \\ y=5.6\text{m}\to \text{cm}=5.6\cdot 100\text{cm}=560\text{cm} \\ 1200=2^4\cdot 3\cdot 5^2 \\ 560=2^4\cdot 5\cdot 7 \\ \text{GCD}(1200,560)=2^4\cdot 5=80 \\ a=GCD(x,y)=GCD(1200,560)=80\text{cm} \\ {S}_1=x\cdot y=1200\cdot 560=672000{\text{cm}}^2 \\ {S}_2=a\cdot a=80\cdot 80=6400{\text{cm}}^2 \\ n=S_1/S_2=672000/6400=105 \end{gathered}$$

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