What is a Perfect Number? Definition and Examples


What is a perfect number? A perfect number is a number that is equal to the sum of its proper factors. Let us show that 6 is a perfect number.

The factors of 6 are 1, 2, 3, and 6.

The proper factors of 6 are 1, 2, and 3.

The sum of the proper factors of 6 is 1 + 2 + 3 = 3 + 3 = 6.

Therefore, 6 is a perfect number since 1 + 2 + 3 = 6.

In fact, 6 is the smallest perfect number

7 is not a perfect number since its only proper factor is 1. Notice also that 7 is a prime number. We can then conclude that prime numbers cannot be perfect numbers.

Is 8 a perfect number?


The proper factors of 8 are 1, 2, and 4.

1 + 2 + 4 is not equal to 8. Therefore, 8 is not a perfect number.

9, 10, 11, 12, 13, 14, and 15 are not perfect numbers either.

Is 16 a perfect number?


The proper factors of 16 are 1, 2, 4, and 8.

1 + 2 + 4 + 8 is not equal to 16. Therefore, 16 is not a perfect number either.

What is the next perfect number after 6?


The next perfect number after 6 is 28.

The proper factors of 28 are 1, 2, 4, 7, and 14.

1 + 2 + 4 + 7 + 14 = 3 + 4 + 7 + 14 = 7 + 7 + 14 = 14 + 14 = 28

Do you want to see more perfect numbers

Recent math words

  1. What is a Vector? Definition and Examples

    Feb 04, 22 05:28 AM

    What is a vector? Definition, explanations and easy to understand read life examples.

    Read More

  2. What are Vertical Angles? Definition and Examples

    Feb 03, 22 05:45 AM

    What are vertical angles? Definition, explanation and easy to understand examples.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: