Square tiles

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

Correct answer:

n =  105
a =  80 cm

Step-by-step explanation:

$$\begin{gathered} 1200=2^4\cdot 3\cdot 5^2 \\ 560=2^4\cdot 5\cdot 7 \\ \text{GCD}(1200,560)=2^4\cdot 5=80 \\ a=GCD(1200,560)=80 \\ n=1200\cdot 560\mathrm{/}{a}^2=1200\cdot 560\mathrm{/}80^2=105 \end{gathered}$$

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