Dividing

Divide the three-line segments 13 cm, 26 cm, and 19.5 cm long for parts so that the individual pieces are equally long and longest. How long will the individual parts take, and how many will there be?

Correct answer:

x =  65 mm
n =  9

Step-by-step explanation:

$$\begin{gathered} a=13\text{cm}\to \text{mm}=13\cdot 10\text{mm}=130\text{mm} \\ b=26\text{cm}\to \text{mm}=26\cdot 10\text{mm}=260\text{mm} \\ c=19.5\text{cm}\to \text{mm}=19.5\cdot 10\text{mm}=195\text{mm} \\ 130=2\cdot 5\cdot 13 \\ 260=2^2\cdot 5\cdot 13 \\ 195=3\cdot 5\cdot 13 \\ \text{GCD}(130,260,195)=5\cdot 13=65 \\ x=GCD(a,b,c)=GCD(130,260,195)=65\text{mm} \end{gathered}$$

$n=(a+b+c)/x=(130+260+195)/65=9$

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