Multiple choice

Find the greatest number which divides 62, 132 and 232 so as to leave the same remainder in each case.

  1. 30

  2. 20

  3. 10

  4. 15

  5. None of these
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C Correct answer
Explanation

Find GCD of (132-62), (232-132), (232-62) = GCD(70, 100, 170) = 10.

AI explanation

The greatest number that leaves the same remainder in each case is the highest common factor of the differences between the numbers. We calculate the differences as 132 minus 62 equals 70, 232 minus 132 equals 100, and 232 minus 62 equals 170. The highest common factor of 70, 100, and 170 is 10.

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