A natural number n is called perfect when the sum of all its (positive) divisors lower than n itself equals n .
Is 6 a perfect number?
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All positive divisors of 6 that is lower than 6 is 1 , 2 , and 3 . 1 + 2 + 3 = 6 . So 6 is a perfect number. (You can also use the formula "If 2 p − 1 is prime, 2 p − 1 ( 2 p − 1 ) is perfect." Since 6 = 2 2 − 1 ( 2 2 − 1 ) , 6 is a perfect number.
6 = ( 2 2 − 1 ) ( 2 2 − 1 ) So it is perfect
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The divisors of 6 , lower than 6 itself are 3 . Namely 1 , 2 and 3 . Summing these divisors we have 1 + 2 + 3 = 6 so, by definition, 6 is a perfect number . :) Enjoy!