Multiple choice

The greatest number which divides 43, 91 and 183 and leaves the same remainder in each case is

  1. 7

  2. 4

  3. 220

  4. 23
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B Correct answer
Explanation

If a number divides 43, 91, and 183 leaving the same remainder, it must divide the differences: 91 - 43 = 48, 183 - 91 = 92, and 183 - 43 = 140. The greatest common divisor of 48, 92, and 140 is 4.

AI explanation

By the common remainder theorem, the greatest such number is the highest common factor of the differences between the numbers. The differences are 91 - 43 = 48 and 183 - 91 = 92. The highest common factor of 48 and 92 is 4. The result is 4.

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