Gardens colony

The garden's colony, with dimensions of 180 m and 300 m, is to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.

Correct answer:

n =  15
c =  60 m

Step-by-step explanation:

$$\begin{gathered} a=180\text{m} \\ b=300\text{m} \\ 180=2^2\cdot 3^2\cdot 5 \\ 300=2^2\cdot 3\cdot 5^2 \\ \text{GCD}(180,300)=2^2\cdot 3\cdot 5=60 \\ c=GCD(180,300)=60\text{m} \\ S=a\cdot b=180\cdot 300=54000{\text{m}}^2 \\ {S}_1=c^2=60^2=3600{\text{m}}^2 \\ n=S/S_1=54000/3600=15 \end{gathered}$$

$c=60=60\text{m}$

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