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?

Answer 1

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.