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Imagine you want to cover a rectangle (width: 43 m; height: 17 ) with squares of the same size. So the size of a square can be written as $$s = \frac{43}{a} = \frac{17}{b}$$ with $a, b$ being positive integers. How can you now calculate possible solutions for $s$?

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The Euklidean algorithm applied to $43\,\mathrm m$ and $17\,\mathrm m$ finds a greatest common divisor of $1\,\mathrm m$ (fortunately the lengths are at least commensurable). Thus $s$ can be any divisor of $1\,\mathrm m$ (i.e. $1\,\mathrm m$, $\frac12\,\mathrm m$, $\frac13\,\mathrm m$, $\frac14\,\mathrm m$, and so on)

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