Sheet metal cutting

The plumbers have to cut sheet metal measuring 220 cm and 308 cm into squares of equal size so that the squares are as large as possible and the sheet metal is used without residue. How many such squares will they cut? Determine the side of this square.

Final Answer:

x =  44 cm
n =  35

Step-by-step explanation:

$$\begin{gathered} a=220\text{cm} \\ b=308\text{cm} \\ 220=2^2\cdot 5\cdot 11 \\ 308=2^2\cdot 7\cdot 11 \\ \text{GCD}(220,308)=2^2\cdot 11=44 \\ x=GCD(a,b)=GCD(220,308)=44\text{cm} \end{gathered}$$

$n=a/x\cdot b/x=220/44\cdot 308/44=35$

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