Dividing

Divide the three line segment 13 cm, 26 cm and 19.5 cm long for parts so that the individual parts were equally long and longest. How long will the individual parts and how many it will?

Result

x =  5 cm
n =  115

Solution:

$130=2 \cdot 5 \cdot 13 \ \\ 250=2 \cdot 5^3 \ \\ 195=3 \cdot 5 \cdot 13 \ \\ \text{GCD}(130, 250, 195)=5 \ \\ \ \\ x=GCD(130, 250, 195)=5 \ \text{cm}$

$n=(130+250+195)/x=(130+250+195)/5=115$

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