Square gardens

The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square.

Correct result:

a =  60 m
n =  15

Solution:

$$\begin{gathered} x=180\text{ m } \\ y=300\text{ m } \\ 180=2^2\cdot 3^2\cdot 5 \\ 300=2^2\cdot 3\cdot 5^2 \\ \text{GCD}(180,300)=2^2\cdot 3\cdot 5=60 \\ a=GCD(x,y)=GCD(180,300)=60\text{ m} \end{gathered}$$

$n=x\mathrm{/}a\cdot (y\mathrm{/}a)=180\mathrm{/}60\cdot (300\mathrm{/}60)=15$

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