Amina had 26 Dark chocolates and 65 Milk chocolates. She wants to distribute an equal number of chocolates of either kind to her friends. What is the maximum number of chocolates a friend of hers can receive? [4 marks]

Solution:

Amina wants to distribute an equal number of chocolates of either kind to her friends.
The number of chocolates distributed must be a common factor of 26 and 65.

Since the question is asking for the maximum number of chocolates a person can receive, we will be looking for the largest common factor of 26 and 65 = HCF(26 , 65) [1 mark]

Factors of 26 = 1, 2, 13, 26 [0.5 marks]
Factors of 65 = 1, 5, 13, 65 [0.5 marks]
Common factors = 1, 13 [0.5 marks]
HCF = 13 [0.5 marks]

Thus, the maximum number of chocolates a person can receive is 13. [1 mark]