Question

Peter has $12$ pens, and Sheldon has $15$ pens. They wanted to make bundles of pens, having the same number of pens in each bundle. How many maximum possible pens can be included in each bundle if all the bundles are identical?

• A. $4$
• B. $5$
• C. $3$
• D. $2$

Answer 1

The correct option is C $3$

Number of pens Peter has $=12$
Number of pens Sheldon has $=15$
The number of pens in each bundle is the same.
$\therefore$ Number of pens in each bundle must be a common factor of $12$ and $15.$
For maximum number of pens in each bundle, we need to evaluate the GCD of $12$ and $15.$

Finding the GCD of $12$ and $15$ using step diagram method we get,



$12=2\times 2\times 3$
$15=3\times 5$
GCD is $3$.

$\therefore 3$ pens can be included in each bundle.