2. The product of two natural numbers is 2,538. If one of the numbers is reduced by 6, and the other remains the same, then their product is 2,214. What are these numbers?
First method:

Let the required natural numbers be denoted by $x$ and $y$. It holds that $x \cdot y=2538$. 1 POINT

If we decrease the number $x$ by 6, the new number has the value $x-6$. 1 POINT

It holds that $(x-6) \cdot y=2214$. 1 POINT

This can be written as $x \cdot y-6 \cdot y=2214$. 1 POINT

Using the known value of the product $x \cdot y$, we get $2538-6 y=2214, \quad 1$ POINT

which simplifies to $6 y=2538-2214=324, \quad 1$ POINT

so it follows that $y=324: 6=54$. 2 POINTS

Then $x=2538: 54=47$. 2 POINTS

TOTAL 10 POINTS