## Task 4 - 010924

The product of four consecutive natural numbers is equal to 93024.

What are the numbers?
Let $n$ be the smallest of the four numbers. Since $10^{4}=1000093024$, it follows that $7<n<20$. As 5 is not a divisor of 93024, $n$ must leave a remainder of 1 when divided by 5. Therefore, $n$ can only be $\{11,16\}$.

Since $93024=2^{5} \cdot 3^{2} \cdot 17 \cdot 19$, 17 and 19 must be among the numbers $n, n+1, n+2$, and $n+3$. Thus, $n=16$.

Verification: $16 \cdot 17 \cdot 18 \cdot 19=93024$.