# Perfect number

What is a perfect number? A number is perfect if the sum of its proper factors is equal to the number.

To find the proper factors of a number, write down all numbers that divide the number with the exception of the number itself.

The proper factors of 18 are 1, 2, 3, 6, and 9

If the sum of the factors is equal to 18, then 18 is a perfect number.

1 + 2 + 3 + 6 + 9 = 6 + 6 + 9 = 12 + 9 = 21

Therefore, 18 is not perfect.

Another example: Find out if  496 is  a perfect number

The proper factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, and 248

1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496

496 is perfect.

The first 10 perfect numbers are shown below. Notice that after the fourth one, they get pretty big faster.

6

28

496

8128

33550336

8589869056

137438691328

2305843008139952128

2658455991569831744654692615953842176

191561942608236107294793378084303638130997321548169216

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