Largest squares

How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?

Correct answer:

n =  6

Step-by-step explanation:

$$\begin{gathered} a=16\text{ dm } \\ b=96\text{ dm } \\ 16=2^4 \\ 96=2^5\cdot 3 \\ \text{GCD}(16,96)=2^4=16 \\ c=GCD(a,b)=GCD(16,96)=16\text{ dm } \\ n=(a\mathrm{/}c)\cdot (b\mathrm{/}c)=(16\mathrm{/}16)\cdot (96\mathrm{/}16)=6 \end{gathered}$$

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