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Find the sum of reciprocal of all positive integers that divide 2424

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Full solution

Q. Find the sum of reciprocal of all positive integers that divide 2424
  1. Identify divisors of 2424: Identify all positive integers that divide 2424. \newlineDivisors of 2424: 11, 22, 33, 44, 66, 88, 1212, 2424.
  2. Calculate reciprocals: Calculate the reciprocal of each divisor.\newlineReciprocals: 11\frac{1}{1}, 12\frac{1}{2}, 13\frac{1}{3}, 14\frac{1}{4}, 16\frac{1}{6}, 18\frac{1}{8}, 112\frac{1}{12}, 124\frac{1}{24}.
  3. Add reciprocals: Add all the reciprocals together.\newlineSum: 11+12+13+14+16+18+112+124.\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} + \frac{1}{12} + \frac{1}{24}.
  4. Simplify sum: Simplify the sum using common denominator.\newlineCommon denominator = 2424.\newlineSum: 2424+1224+824+624+424+324+224+124=6024\frac{24}{24} + \frac{12}{24} + \frac{8}{24} + \frac{6}{24} + \frac{4}{24} + \frac{3}{24} + \frac{2}{24} + \frac{1}{24} = \frac{60}{24}.

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