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

SOLUTION :  

We need to find the HCF of 144 & 90 to find the greatest number of cartons, each stack would have.

Given:  

Number of cartons of coke cans = 144

Number of cartons of Pepsi cans = 90.

H.C.F. of 144 and 90.

By applying Euclid’s division lemma ,a = bq +r.

Let a = 144 and b = 90

144 = 90 x 1 + 54

90 = 54 x 1+ 36

54 = 36 x 1 + 18

36 = 18 x 2 + 0

H.C.F. =18.

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

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Given : 144 cartons of Coke cans and 90 cartons of Pepsi cans are stacked.

Here, we have to find Greatest number of cartons each stack would have.

Prime factorization of 144 = 3^2 * 2^4

Prime factorization of 90 = 3^2 * 2 * 5.

HCF(144,90) = 3^2 * 2

                    = 18.

Therefore, the greatest number of cartons in each stack = 18.

Hope it helps!