Perfect (English)
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Definition (keystage 2)
A perfect number is equal to the sum of its divisors; eg
6 = 1 + 2 + 3,
28 = 1 + 2 + 4 + 7 + 14
Not many perfect numbers are known, because they become very big very soon. But there is a formula for generating some of them, known since Euclid's time: add together a series of powers of 2 until you get a prime number, and then multiply by the last power of two you used.
eg, 20+21+22=1+2+4=7, which is prime; multiply by 4 to get 28, which is perfect.
All the known perfect number are even.
6 = 1 + 2 + 3,
28 = 1 + 2 + 4 + 7 + 14
Not many perfect numbers are known, because they become very big very soon. But there is a formula for generating some of them, known since Euclid's time: add together a series of powers of 2 until you get a prime number, and then multiply by the last power of two you used.
eg, 20+21+22=1+2+4=7, which is prime; multiply by 4 to get 28, which is perfect.
All the known perfect number are even.
Relations
- broader:
- (en) Property of number or variable
- references:
- (en) Proper divisor
- referenced:
- (en) Imperfect
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