Gardens colony

Gardens colony with dimensions of 180 m and 300 m are 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.

Result

n =  15
c =  60 m

Solution:

a=180 m b=300 m 180=22325 300=22352 GCD(180,300)=2235=60  c=GCD(180,300)=60 m S=a b=180 300=54000 m2 S1=c2=602=3600 m2 n=S/S1=54000/3600=15a=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
c=60 mc=60 \ \text{m}



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