The King

The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?

Correct answer:

n =  3
r =  14
d =  15

Step-by-step explanation:

$$\begin{gathered} 42=2\cdot 3\cdot 7 \\ 45=3^2\cdot 5 \\ \text{GCD}(42,45)=3 \\ n=GCD(42,45)=3 \end{gathered}$$

$r=42\mathrm{/}n=42\mathrm{/}3=14$

$d=45\mathrm{/}n=45\mathrm{/}3=15$

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