Question

There are $21$ pencils and $14$ erasers that need to be packed in pencil boxes. Each pencil box must have equal number of pencil and eraser. Find the maximum number of such boxes.

Answer 1

We need to find the maximum number of boxes that holds equal number of pencil and erasers in each box.

Hence, we need to find the greatest common divisor of $21$ and $14.$

Factor tree of $21$ and $14$ are as follows:
$\therefore 21=3\times 7$
And, $14=2\times 7$
GCD = $7$
If we put 3 pencil and 2 erasers in each box, then 21 pencils and 14 erasers can be put into 7 boxes.
Hence, the required number of maximum boxes is $7.$