To calculate the drop factor, we need to determine the number of drops per milliliter (gtts/mL) that the administration set delivers.

First, we need to convert the time from minutes to hours: 30 minutes = 30/60 = 0.5 hours

Next, we calculate the total volume delivered per hour: 100 mL / 0.5 hours = 200 mL/hour

Now, we can calculate the number of drops delivered per hour: 200 mL/hour * 25 gtts/mL = 5000 gtts/hour

Finally, we calculate the drop factor by dividing the number of drops per hour by 60 (minutes): 5000 gtts/hour / 60 minutes = 83.33 gtts/minute

Therefore, the drop factor for the administration set is 83.33 gtts/minute.