Question

What is a perfect number? Is 496 a perfect number?

Answer 1

A number for which sum of all its factors is equal to twice the number is called a perfect number.

To find if a number is a perfect number or not first we need to find out all the factors of the number.
So,
1$\times$496 = 496
2$\times$248 = 496
4$\times$124 = 496
8$\times$62 = 496
16$\times$31 = 496
The various factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496.
Now sum of all the factors= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 + 496 = 992 = 2$\times$496
Hence, the sum of all the factors of the of 496 is twice the number.
$\therefore$496 is a perfect number.