2. The product of four consecutive even natural numbers is 13440. Determine these numbers.
Solution. Let the consecutive even numbers be $2 n, 2 n+2$, $2 n+4$ and $2 n+6$. Then

$$
2 n(2 n+2)(2 n+4)(2 n+6)=13440
$$

from which we get

$$
n(n+1)(n+2)(n+3)=840=2^{3} \cdot 3 \cdot 5 \cdot 7
$$

Since 5 and 7 are prime numbers, one of the factors must be the number $6=2 \cdot 3$, and the other factor is $2 \cdot 2=4$. Therefore,

$$
n(n+1)(n+2)(n+3)=4 \cdot 5 \cdot 6 \cdot 7
$$

so the required numbers are $8,10,12$ and 14.