1. The problem is to understand what an improper divisor is. 2. In mathematics, a divisor (or factor) of a number is a number that divides it exactly without leaving a remainder. 3. An improper divisor of a number is a divisor that is equal to the number itself. 4. For example, for the number 6, its divisors are 1, 2, 3, and 6. 5. Here, 6 is an improper divisor of itself because it divides 6 exactly and is equal to 6. 6. Proper divisors are all divisors of a number except the number itself. 7. So, improper divisor means the divisor that is the number itself.