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

144 cartons of coke cans and 90 cartons of pepsi cans are to be stacked in a canteen. If each stack is of same height and is to contain cartons of the

Question

$144$ cartons of coke cans and $90$ cartons of pepsi cans are to be stacked in a canteen. If each stack is of 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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Solution

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Correct option is A)

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 $90$ .

$144 = 90$ $\times$ $1 + 54$
$90 = 54$ $\times$ $1 + 36$
$54 = 36$ $\times$ $1 + 18$
$36 = 18$ $\times$ $2 + 0$

So, the H.C.F. of $144$ and $90$ is $18$ .
Number of cartons in each stack $= 18 .$

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