Question

Is $8128$ a perfect number?

Answer 1

Step $1$: Definition of Perfect Numbers:

Perfect Numbers: A given number is a perfect number if the sum of all its factors equals twice the number.

Step $2$: Finding the factors of $8128$.

Factors :$1,2,4,8,16,32,64,127,254,508,1016,2032$ and $4064$.

Step $3$: Finding the sum of all the factors

Sum of all the factors: $1+2+4+8+16+32+64+127+254+508+1016+2032+4064+8128$$=8128+8128=8128\times 2=16256$

Since, sum of the factors of $8128$ equals twice of $8128$$=16256$

Hence, $8128$ is a perfect number.