Two pieces

Two pieces of cloth 15 and 20 meters long are to be cut into small pieces of equal lengths. What will be the greatest length of each piece?

Correct answer:

x =  500 cm

Step-by-step explanation:

$$\begin{gathered} a=15\text{m}\to \text{cm}=15\cdot 100\text{cm}=1500\text{cm} \\ b=20\text{m}\to \text{cm}=20\cdot 100\text{cm}=2000\text{cm} \\ 1500=2^2\cdot 3\cdot 5^3 \\ 2000=2^4\cdot 5^3 \\ \text{GCD}(1500,2000)=2^2\cdot 5^3=500 \\ x=GCD(a,b)=GCD(1500,2000)=500\text{cm} \end{gathered}$$

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