Question

What is a perfect number? Is 496 a perfect number? [4 MARKS]

Answer 1

Definition: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

A number for which sum of all its factors is equal to twice the number is called a perfect number.
We have to find out if 496 is a perfect number or not.
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.