Tshegofatso is putting together packages of food as gifts for her friends. Tshegofatso has 330 sweets and 231 chocolates. Tshegofatso wants to create identical packages of food, and she must use all of the food. What is the greatest number of identical packages that Tshegofatso can make, if it is given that: - \( 330=2 \times 3 \times 5 \times 11 \) - \( 231=3 \times 7 \times 11 \)

To find the greatest number of identical packages Tshegofatso can create using all the sweets and chocolates, we need to determine the greatest common divisor (GCD) of 330 and 231. Looking at the prime factorizations, \( 330 = 2 \times 3 \times 5 \times 11 \) and \( 231 = 3 \times 7 \times 11 \), we can identify the common prime factors. The common factors are \( 3 \) and \( 11 \). Now, multiply these common factors together: \( GCD = 3 \times 11 = 33\). Thus, Tshegofatso can create **33 identical packages** using all of her sweets and chocolates! Now she knows she’ll have to pack 10 sweets and 7 chocolates in each package to utilize all her food items perfectly. How delightful!