Perfect Numbers
Definition of a Perfect Number:
A number which is equal to the sum of its factors other than
itself is called a perfect number.
Solved Examples:
1. Verify that 6 and 28 are perfect numbers.
Solution:
Factors of 6 are 1, 2, 3,6.
Sum of factors of 6 other than
6 = 1 + 2 + 3 = 6 (number itself).
Factors of 28 are 1, 2, 4, 7, 14, 28.
Sum of
factors of 28 other than 28 = 1 + 2 + 4 + 7 + 14 = 28 (number itself).
Thus, 6
and 28 are the perfect numbers. Hence verified.
2. Verify that 496 is a perfect number.
Solution:
Factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496
Sum of factors of 496 other than 6 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496 (number itself).
Thus, 496 are the perfect numbers. Hence verified.
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