CDS 2026 (I) Elementary Mathematics, question 27

Topic: Number system

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Q27

What is the sum of all the divisors of 256256 ?

  1. (a) 511511Correct answer
  2. (b) 510510
  3. (c) 256256
  4. (d) 255255

Solution.

Answer: (a) 511511

  1. Since 256=28256 = 2^{8}, its positive divisors are 1,2,221,2,2^{2}, …, 282^{8}.
  2. Their geometric sum is (29−1)/(2−1)=511\left( 2^{9} - 1 \right)/(2 - 1) = 511.