To find out how much flour the factory will use for 72 batches of cookies, we can multiply the amount of flour used per batch by the number of batches.
Given that the factory uses \( \frac{1}{2} \) of a barrel of flour for each batch, we can calculate the total flour used for 72 batches as follows:
\[ \text{Total flour} = \text{Flour per batch} \times \text{Number of batches} \] \[ \text{Total flour} = \frac{1}{2} \times 72 \]
To perform this calculation:
\[ \frac{1}{2} \times 72 = \frac{72}{2} = 36 \]
Thus, the factory will use \( 36 \) barrels of flour for 72 batches.
The final answer is:
\[ \text{Total flour used} = 36 \text{ barrels} \]