Container

The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?

Correct result:

x =  65 cm

Solution:

$$\begin{gathered} a=3.9\text{ m}\to \text{ cm}=3.9\cdot 100\text{ cm}=390\text{ cm } \\ b=3.25\text{ m}\to \text{ cm}=3.25\cdot 100\text{ cm}=325\text{ cm } \\ c=2.6\text{ m}\to \text{ cm}=2.6\cdot 100\text{ cm}=260\text{ cm } \\ 390=2\cdot 3\cdot 5\cdot 13 \\ 325=5^2\cdot 13 \\ 260=2^2\cdot 5\cdot 13 \\ \text{GCD}(390,325,260)=5\cdot 13=65 \\ x=GCD(a,b,c)=GCD(390,325,260)=65\text{ cm} \end{gathered}$$

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