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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