Why Are Some Numbers Magic? The Secret of Perfect Numbers

Imagine you have a special group of friends. A perfect number is like that friend who always shares evenly with everyone, if you add up all the people in their group, it matches the total number of candies they had. For example, the number 6 has divisors 1, 2, and 3. If we add those up: 1 + 2 + 3 = 6! That makes 6 a perfect number because it's equal to the sum of its parts.

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Examples

  1. If you have a bag of 6 candies and share them with friends who take 1, 2, or 3 candies each, you give out all the candies exactly.
  2. Adding up the numbers that divide evenly into 28 gives back the same number: $1 + 2 + 4 + 7 + 14 = 28$.
  3. The smallest perfect number is 6, it has just three divisors (excluding itself) and adds to the same total.

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