A store sells boxes of Garth bought 18 boxes, Rico bought 36 boxes, and Mai bought 45 boxes. What is the greatest number of boxes in each pack? How many packs did each person buy if each box contained the greatest number of boxes possible?

To determine the greatest number of boxes in each pack and the number of packs each person bought, we'll follow these steps: 1. **Identify the Number of Boxes Each Person Bought:** - **Garth:** 18 boxes - **Rico:** 36 boxes - **Mai:** 45 boxes 2. **Find the Greatest Common Divisor (GCD):** The greatest number of boxes per pack must be a number that evenly divides into each person's total number of boxes. This number is the **GCD** of 18, 36, and 45. - **Prime Factorization:** - 18 = 2 × 3² - 36 = 2² × 3² - 45 = 3² × 5 - **GCD Calculation:** - The common prime factor is 3² (which is 9). - Therefore, **GCD = 9**. 3. **Determine the Number of Packs Each Person Bought:** - **Garth:** 18 boxes ÷ 9 boxes/pack = **2 packs** - **Rico:** 36 boxes ÷ 9 boxes/pack = **4 packs** - **Mai:** 45 boxes ÷ 9 boxes/pack = **5 packs** --- **Summary:** - **Greatest number of boxes per pack:** 9 boxes - **Number of packs bought:** - Garth: 2 packs - Rico: 4 packs - Mai: 5 packs