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?

Result

x =  65 cm

Solution:

a=3.9 m→cm=3.9⋅ 100 cm=390 cm b=3.25 m→cm=3.25⋅ 100 cm=325 cm c=2.6 m→cm=2.6⋅ 100 cm=260 cm  390=2⋅3⋅5⋅13 325=52⋅13 260=22⋅5⋅13 GCD(390,325,260)=5⋅13=65  x=GCD(a,b,c)=GCD(390,325,260)=65 cma=3.9 \ m \rightarrow cm=3.9 \cdot \ 100 \ cm=390 \ cm \ \\ b=3.25 \ m \rightarrow cm=3.25 \cdot \ 100 \ cm=325 \ cm \ \\ c=2.6 \ m \rightarrow cm=2.6 \cdot \ 100 \ cm=260 \ 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}

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