Sum of Factors

Level 2

What is the sum of the factors of 256?

511 504 513 512

Rishabh Ghosh by Rishabh Ghosh , 21, USA

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1 solution

Anuj Shikarkhane
Jul 1, 2014

The factors of 256 are 1,2,4,8,16,32,64,128,256.After adding these numbers you will get the sum as 511.(You don't have to count 16 twice).

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Note that, since 256 = 2 8 256 = 2^{8} , the factors of 256 256 will be of the form 2 k 2^{k} for 0 ≤ k ≤ 8 0 \le k \le 8 . Thus their sum will be

∑ k = 0 8 2 k = 2 9 − 1 = 511 \displaystyle\sum_{k=0}^{8} 2^{k} = 2^{9} - 1 = 511 .

Brian Charlesworth - 6 years, 6 months ago

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Wow! Your way to solve this problem is a way better than mine.

Anuj Shikarkhane - 6 years, 6 months ago

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