## Task 1 - 030721

By what highest power of 2 is the product of four consecutive even natural numbers at least divisible?
Among four consecutive natural numbers, there is always exactly one that is divisible by 4 and exactly one other that is divisible by 2 but not by 4.

Therefore, among the four consecutive even natural numbers, there is always exactly one that is divisible by 8 and exactly one other that is divisible by 4 but not by 8.

The other two even numbers are in each case divisible by 2 but not by 4. Thus, the considered product is divisible by $8 \cdot 4 \cdot 2 \cdot 2=2^{7}$.

Since among the four consecutive even numbers, none must be divisible by 16, the product is generally not divisible by $2^{8}$. The highest power sought is therefore $2^{7}$.