Multiple choice

Let "k" be the number of factors (excluding $1$ and the expression itself) of the number 38808 and "m" be the sum of its divisors. Let "h" be the remainder of m/k. Find the sum of the digits of "h" ?

  1. $1$
  2. $0$
  3. $2$
  4. $5$
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A Correct answer
AI explanation

The prime factorization of 38808 is 2 cubed multiplied by 3 squared multiplied by 7 cubed. The total number of factors is (3 plus 1) multiplied by (2 plus 1) multiplied by (3 plus 1), which equals 48, so k is 46 after excluding 1 and the number itself. The sum of the divisors, m, is (1 plus 2 plus 4 plus 8) multiplied by (1 plus 3 plus 9) multiplied by (1 plus 7 plus 49 plus 343), which equals 15 multiplied by 13 multiplied by 400, giving 78000. Dividing 78000 by 46 gives a remainder of 10, making h equal to 10. The sum of the digits of h is 1 plus 0, which equals 1.