Multiple choice

A number divides 12288, 28200 and 44333 so as to leave the same remainder in each case. What is that number?

  1. 272

  2. 232

  3. 221

  4. 120
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C Correct answer
Explanation

The number must be the HCF of the differences: (28200-12288)=15912, (44333-28200)=16133, and (44333-12288)=32045. Calculating the HCF of 15912 and 16133 yields 221.

AI explanation

Using the Euclidean algorithm, the required number that leaves the same remainder in each case is a common factor of the differences between the numbers. The differences are 28200 minus 12288 equals 15912, 44333 minus 28200 equals 16133, and 44333 minus 12288 equals 32045. The highest common factor of these three differences is 221, which divides the differences without leaving a remainder and is the required number.

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