Wall marble tiles

We want to cover a wall with dimensions of 4 m x 250 cm with square marble tiles with the largest possible dimensions of the sides of the tiles so that there are no losses caused, for example, by cutting them during tiling.
How many tiles will we need for the whole wall?

Final Answer:

n =  40

Step-by-step explanation:

$$\begin{gathered} a=4\text{m}\to \text{cm}=4\cdot 100\text{cm}=400\text{cm} \\ b=250\text{cm} \\ 400=2^4\cdot 5^2 \\ 250=2\cdot 5^3 \\ \text{GCD}(400,250)=2\cdot 5^2=50 \\ x=GCD(a,b)=GCD(400,250)=50\text{cm} \\ {n}_1=a/x=400/50=8 \\ {n}_2=b/x=250/50=5 \\ n=n_1\cdot n_2=8\cdot 5=40 \end{gathered}$$

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