Greatest Number of Cartons in Each Stack for 144 Coke and 90 Pepsi Cartons

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: 144 cartons of Coke cans and 90 cartons of Pepsi cans are to be stacked in a canteen. If each stack is of the same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack would have?

Step 1: Identify the Mathematical Concept

The greatest number of cartons in each stack will be the HCF (Highest Common Factor) of 144 and 90.

Step 2: Find the HCF Using Euclid’s Division Algorithm

144 = 90 × 1 + 54

90 = 54 × 1 + 36

54 = 36 × 1 + 18

36 = 18 × 2 + 0

Since the remainder is zero,

∴ HCF (144, 90) = 18

Final Answer

∴ The greatest number of cartons in each stack is 18.

Conclusion

Thus, by using Euclid’s division algorithm, we find that each stack can have a maximum of 18 cartons.