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?

Answer 1

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 $=18.$