# 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 result:

n =  105
a =  80 cm

#### Solution:

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

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