Dividing Lines into Parts

Divide three lines with lengths of 12 cm, 24 cm, and 64 cm into equally long and, at the same time, the most extended possible parts. How long will the individual parts be, and how many will there be?

Final Answer:

x =  4 cm
n =  25

Step-by-step explanation:

$$\begin{gathered} a=12 \\ b=24 \\ c=64 \\ 12=2^2\cdot 3 \\ 24=2^3\cdot 3 \\ 64=2^6 \\ \text{GCD}(12,24,64)=2^2=4 \\ x=GCD(a,b,c)=GCD(12,24,64)=4\text{cm} \end{gathered}$$

$n=(a+b+c)/x=(12+24+64)/4=25$

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