Multiple choice

Which one of the following three-digit numbers divides $9238$ and $7091$ with the same remainder in each case?

  1. $113$
  2. $209$
  3. $317$
  4. $191$
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A Correct answer
Explanation

If a number n divides both 9238 and 7091 with the same remainder, then n must divide their difference, 9238 - 7091 = 2147. Factoring 2147 gives 19 * 113. Since 113 is a three-digit number, it is the answer.

AI explanation

Subtract the smaller number from the larger one to get 9238 minus 7091 equals 2147. The required three-digit number must be a factor of 2147. Factoring 2147 reveals that 113 times 19 equals 2147, making 113 the required divisor.

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