Multiple choice

The largest number which divides 62, 132 and 237 to leave the same remainder in each case is:

  1. 51

  2. 35

  3. 8

  4. 53
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B Correct answer
Explanation

Find the GCD of differences: (132-62)=70, (237-132)=105, (237-62)=175. GCD(70, 105, 175) = 35.

AI explanation

If a number divides multiple values to leave the same remainder, it must perfectly divide the differences between those values. Calculate the differences as 132 minus 62 to get 70, and 237 minus 132 to get 105. The required number is the highest common factor of 70 and 105. The highest common factor of 70 and 105 is 35.

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