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? 

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