Question

A gift shopkeeper has 45 identical balls, 50 identical toys, 30 identical flowers and 35 identical sweeets. He decides to make maximum number of identical giftboxes having all given items. The total number of items in each giftbox would be .

Answer 1

To find the maximum number of identical gift boxes, we need to evaluate GCD of given number of items.

Prime factorization of $45,50,35\&30$ are as follows:
$\to 45=3\times 3\times 5$
$\to 50=2\times 5\times 5$
$\to 30=2\times 3\times 5$
$\to 35=5\times 7$

The greatest common factors or GCD among these is $5$.

Hence, the maximum number of giftboxes is $5.$

There are total $45$ identical balls.
$\therefore$ Number of balls in each box
$=\frac{\text{Total number of balls}}{\text{Number of giftboxes}}$
$=\frac{45}{5}=9\text{balls}$.

Similarly, the number of toys, flowers and sweets are $10,6\&7$ respectively.

$\therefore$ There are total $9+10+6+7=32$ items in each giftbox.