Problem 3. In a warehouse, there are 360 boxes of apples and 384 boxes of pears. The boxes of fruit need to be delivered to different stores in shipments where there is always the same number of fruit boxes and in each shipment, there is the same number of apple boxes. The trucks used to transport the fruit shipments can carry a maximum of 60 boxes. How many boxes of apples and how many boxes of pears are there in each shipment?
Solution. Let $x$ be the number of shipments that need to be delivered. Since each shipment contains an equal number of baskets of fruit, and an equal number of baskets of apples, we conclude that each shipment also contains an equal number of baskets of pears. Therefore, $x \mid 360$ and $x \mid 384$, from which we conclude that $x \mid \operatorname{GCD}(360,384)=24$. If $x=24$, then in each shipment there are $360: 24=15$ baskets of apples and $384: 24=16$ baskets of pears, and since $15+16=31$, but each truck can carry at most 30 baskets of fruit.

Finally, the fruit will be delivered in 24 shipments, and in each shipment there will be 15 baskets of apples and 16 baskets of pears.