# 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:

$a = 180 \ m \ \\ b = 300 \ m \ \\ 180 = 2^2 \cdot 3^2 \cdot 5 \\ 300 = 2^2 \cdot 3 \cdot 5^2 \\ \text{GCD}(180, 300) = 2^2 \cdot 3 \cdot 5 = 60\\ \ \\ \ \\ c = GCD(180, 300) = 60 \ m \ \\ S = a \cdot \ b = 180 \cdot \ 300 = 54000 \ m^2 \ \\ S_{ 1 } = c^2 = 60^2 = 3600 \ m^2 \ \\ n = S/S_{ 1 } = 54000/3600 = 15$
$c = 60 = 60 \ \text { m }$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Do you want to calculate greatest common divisor two or more numbers? Do you want to convert area units? Do you want to convert length units?

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