Question

A positive integer n is perfect if it is the sum of all ifs positive factors except n itself. 15. Show that 496 is perfect.

Answer 1

The sum of all positive factors of 496, except for the number itself, equals 496. This confirms that 496 is a perfect number.

Step-by-step explanation:

To show that 496 is a perfect number, we must demonstrate that it is equal to the sum of all its positive factors, excluding itself. The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, and 496. When we add up all the factors excluding 496 itself, we get:

1. 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496

Thus, since the sum of its non-self factors is equal to the number itself, we can conclude that 496 is a perfect number.