what is the sum of the distinct positive divisors of 1024?

Question

The answer is 2047 and I don't know if there is a fast way to solve this.

Answer 1

Draw a factor tree

 

1024 = 2 x 512

         = 2 x 2 x 256

         = 2 x 2 x 2 x 128

         = 2 x 2 x 2 x 2 x 64

         = 2 x 2 x 2 x 2 x 2 x 32

          = 2 x 2 x 2 x 2 x 2 x 2 x 16

          = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 8

          = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 4

          = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

 

So the positive divisors are the positive integers that divide into 1024 evenly:

 They are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024

 

The total of these is 2047