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In the case of $$\frac{15}3 = 5$$ we have to recognize that whatever properties one side has, the other has also. So since 5 is a natural number, 15/3 must also be that, because they are equal to eachother.

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Natural numbers are "one", "two", $\dots$. They are concepts. Usually one writes them as $1,2,\dots$. With respect to the set of rules stipulating what one can do with these numbers, we have $$ \frac{15}{3} = 5, $$ say. Hence $15/3$ is a natural number.

You should not mistake a representation of a number for the number itself. There are an infinite number of ways to represent the number $5$, but none of them changes the properties of the number $5$.