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.
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.
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.
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
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