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?

Result

n =  3
r =  14
d =  15

Solution:

42=2⋅3⋅7 45=32⋅5 GCD(42,45)=3  n=GCD(42,45)=342=2 \cdot 3 \cdot 7 \ \\ 45=3^2 \cdot 5 \ \\ \text{GCD}(42, 45)=3 \ \\ \ \\ n=GCD(42,45)=3
r=42/n=42/3=14r=42/n=42/3=14
d=45/n=45/3=15d=45/n=45/3=15

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