Rectangular meadow

Divide the rectangular meadow with dimensions of 1280m and 320m into a square shepherd with the longest possible side of the square. How many square pastures did you divide the meadow?

Final Answer:

x =  320 m
n =  4

Step-by-step explanation:

$$\begin{gathered} a=1280\text{m} \\ b=320\text{m} \\ 1280=2^8\cdot 5 \\ 320=2^6\cdot 5 \\ \text{GCD}(1280,320)=2^6\cdot 5=320 \\ x=GCD(a,b)=GCD(1280,320)=320\text{m} \end{gathered}$$

$$\begin{gathered} S=a\cdot b=1280\cdot 320=409600{\text{m}}^2 \\ {S}_1=x^2=320^2=102400{\text{m}}^2 \\ n=S/S_1=409600/102400=4 \end{gathered}$$

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