Bathroom 3

A bathroom measures 300 × 210 cm. What is the largest square tile size that can be used to cover the floor without cutting, and how many such tiles will be needed?

Final Answer:

x =  30 cm
n =  70

Step-by-step explanation:

$$\begin{gathered} a=300\text{cm} \\ b=210\text{cm} \\ 300=2^2\cdot 3\cdot 5^2 \\ 210=2\cdot 3\cdot 5\cdot 7 \\ \text{GCD}(300,210)=2\cdot 3\cdot 5=30 \\ x=GCD(a,b)=GCD(300,210)=30\text{cm} \end{gathered}$$

$$\begin{gathered} n_1=a/x=300/30=10 \\ {n}_2=b/x=210/30=7 \\ n=n_1\cdot n_2=10\cdot 7=70 \end{gathered}$$

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