Question

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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?
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Answer 1

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Given :-

➪ No. of cartons of Coke Cans = 144

➪ No. of cartons of Pepsi Cans = 90

To Find :-

➪ The greatest number of cartons each stack would have, If each stack is of the same height and is to contain cartons of the same drink.

Solution :-

In order to arrange the cartons of the same drink in the same stack, we have to find the greatest number that divides 144 and 90 exactly.

Using Euclid's division algorithm, to find the H.C.F. of 144 and 90.

144 = 90 × 1 + 54 (remainder = 54 ≠ 0)

90 = 54 × 1 + 36 (36 ≠ 0)

54 = 36 × 1 + 18 (18 ≠ 0)

36 = 18 × 2 + 0 (remainder = 0) and (divisor = HCF = 18)

$\large\boxed{hcf \: = 18}$

So, the H.C.F. of 144 and 90 is 18.

Number of cartons in each stack = 18

@SweetestBitter

Answer 2

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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

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?

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Given :-

➪ No. of cartons of Coke Cans = 144

➪ No. of cartons of Pepsi Cans = 90

To Find :-

➪ The greatest number of cartons each stack would have, If each stack is of the same height and is to contain cartons of the same drink.

Solution :-

In order to arrange the cartons of the same drink in the same stack, we have to find the greatest number that divides 144 and 90 exactly.

Using Euclid's division algorithm, to find the H.C.F. of 144 and 90.

144 = 90 × 1 + 54 (remainder = 54 ≠ 0)

90 = 54 × 1 + 36 (36 ≠ 0)

54 = 36 × 1 + 18 (18 ≠ 0)

36 = 18 × 2 + 0 (remainder = 0) and (divisor = HCF = 18)

$\large\boxed{hcf \: = 18}$

So, the H.C.F. of 144 and 90 is 18.

Number of cartons in each stack = 18

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