Multiple choice

The largest number which divides $245$ and $1029$ leaving remainder $5$ is

  1. $15$
  2. $16$
  3. $5$
  4. $9$
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B Correct answer
Explanation

The number must divide (245 - 5) = 240 and (1029 - 5) = 1024. GCD(240, 1024) = 16.

AI explanation

Using the division algorithm, the required number must divide (245 minus 5) and (1029 minus 5) completely. Thus, we need the highest common factor of 240 and 1024. However, the highest common factor of 240 and 1024 is 16, which does not leave a remainder of 5 when dividing 245 because 245 equals 15 times 16 plus 5, but dividing 1029 by 16 leaves a remainder of 9, making 16 an invalid answer; the problem's wording is mathematically flawed, but following the flawed question logic of finding the greatest common divisor of the differences yields 16.

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