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

Question

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

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?

Share with your friends

Talk Doctor Online in Bissoy App

Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Number of cartons of coke cans = 144
Number of cartons of pepsi cans = 90
∴ The greatest number of cartons in one stock = HCF of 144 and 90
By applying Euclid’s division lemma
144 = 90 × 1 + 54
90 = 54 × 1 + 36
54 = 36 × 1 + 18
36 = 18 × 2 + 0
∴ HCF = 18
Hence the greatest number cartons in one stock = 18

Salim Ahmed Kawsar · Answer 2 · Feb 05, 2023 15:29:48

It’s given that,

Number of cartons of coke cans = 144

Number of cartons of Pepsi cans = 90.

So, the greatest number of cartons in a stack can be found by finding the H.C.F. (144, 90).

Thus, by applying Euclid’s division lemma on 144 and 90, we get

144 = 90 x 1 + 54

90 = 54 x 1 + 36

54 = 36 x 1 + 18

36 = 18 x 2 + 0 (only in this stage the remainder becomes 0)

∴ the H.C.F. should be the last divisor i.e., 18.

Hence, the greatest number of cartons together in one stack is 18.

Salim Ahmed Kawsar · Answer 3 · Feb 05, 2023 15:29:48

To find greatest number of cartons each stack would have, we should find HCF of 144 and 90

Prime factors of 144 = 2 × 2 × 2 × 2 × 3 × 3

Prime factors of 90 = 2 × 3 × 3 × 5

Therefore HCF of 144 and 90 is:

2 × 3 × 3 = 18

Therefore the greatest number of cartons each stack would have is: 18

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

3 Answers