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?

Given: 144 cartons of Coke Cans and 90 cartons of Pepsi Cans are to be stacked in a Canteen.

To find: Here we have to find the greatest number of cartons each stack would have.

Solution:

Number of cartons of coke cans = 144

Number of cartons of Pepsi cans = 90

To find the greatest number of cartons we need to calculate the HCF of 144 and 90.

Using Euclid's division algorithm to find the HCF:

Using Euclid’s lemma to get: 

• $144\ =\ 90\ \times\ 1\ +\ 54$

Now, consider the divisor 90 and the remainder 54, and apply the division lemma to get:

• $90\ =\ 54\ \times\ 1\ +\ 36$

Now, consider the divisor 54 and the remainder 36, and apply the division lemma to get:

• $54\ =\ 36\ \times\ 1\ +\ 18$

Now, consider the divisor 36 and the remainder 18, and apply the division lemma to get:

• $36\ =\ 18\ \times\ 2\ +\ 0$

The remainder has become zero, and we cannot proceed any further. 

Therefore the HCF of 144 and 90 is the divisor at this stage, i.e., 18.

So, the greatest number of cartons in each stack is 18.

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Updated on: 10-Oct-2022

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