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 square's side length.

Correct answer:

a =  60 m
n =  15

Step-by-step explanation:

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

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

Try another example