Question

The children received gift packages from their family members. All the packages consisted of total 54 teddy bears, 81 chocolate pastry, and 135 candies. Each child received the same gift package. The maximum possible number of identical packages prepared was

Answer 1

Number of teddy bears $=54$
Number of chocolate pastry $=81$
Number of candies $=135$

As all the children received the same combination of items, the number of items of each type in each package should be a factor of total number of the respective item type.

However, the maximum number of packages prepared is given by GCD of $54,81$ and $135$.


$54=2\times 3\times 3\times 3$
$81=3\times 3\times 3\times 3$
$135=3\times 3\times 3\times 5$

GCD is $3\times 3\times 3=27$

So, the maximum number of packages prepared is $27$.