Every integer is a divisor of itself. A proper divisor of an integer means a positive divisor other than the integer itself. For
example, the divisors of $8$ are $1,$ $2,$ $4,$ and $8,$ but the proper divisors of $8$ are just $1,$ $2,$ and $4$. What is the smallest positive integer whose proper divisors add up to more than the integer itself?
You would need 6 packages for 27 students because 27 isn't divisible by 5 without a remainder and all students need pencils. So, you would need to bu another package of pencils.
