Tiles

The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.

Correct result:

n =  105
a =  80 cm

Solution:

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

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