Problem of the Day

Chapter 5, Lesson 3

In their study of number theory, Bea and Jay have learned that:

The proper factors of a positive integer are all of its factors except for the integer itself.

If the sum of the proper factors:
= the number, then the number is perfect.
> the number, then the number is abundant.
< the number, then the number is deficient.

Today, Bea and Jay started testing powers of prime numbers to determine if they are perfect, abundant, or deficient. They correctly categorized 34 and 53. What is the correct category for each of these powers of prime numbers? Explain.