Paper squares

The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number.

Correct answer:

x =  23 cm
n =  6

Step-by-step explanation:

$$\begin{gathered} a=69\text{ cm } \\ b=46\text{ cm } \\ 69=3\cdot 23 \\ 46=2\cdot 23 \\ \text{GCD}(69,46)=23 \\ x=GCD(a,b)=GCD(69,46)=23\text{ cm} \end{gathered}$$

$$\begin{gathered} c=a\mathrm{/}x=69\mathrm{/}23=3 \\ d=b\mathrm{/}x=46\mathrm{/}23=2 \\ n=c\cdot d=3\cdot 2=6 \end{gathered}$$

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