Question

Which of the following numbers is a perfect number?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is C

$6$

Explanation for the correct option:

Option (C) : $6$

We know that, a number is said to be a perfect number, if the sum of all the factors of a number is equal to twice the number .

Prime factors of $6$ are $1$, $2$, $3$, and $6$

Sum of these factors $=1+2+3+6=12$. Here, we can observe clearly that the given number $6$ can be written as $2\times 6=12$

Thus, $6$ is the perfect number.

Explanation for the incorrect options:

Option (A): $2$

Prime Factors of $2$ are $1$ and $2$ and Sum of all these factors will be equal to $3$ which is not twice of the given number.

Therefore, it is not the perfect number.

Option (B): $4$

Prime Factors of $4$ are $1$, $2$ and $4$ but Sum of all these factors will be equal to $1+2+4=7$ which is not twice of the given number.

Therefore, it is not the perfect number.

Option (D): $8$

Prime Factors of $8$ are $1$, $2$, $4$ and $8$ but Sum of all these factors will be equal to $1+2+4+8=15$ which is not twice of the given number.

Therefore, it is not the perfect number.

Hence, the correct answer is option (C)