Multiple choice

Find the greatest number which when divides 166, 199 and 298, leaves the same remainder in each case.

  1. 22

  2. 33

  3. 66

  4. 69

  5. None of these
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B Correct answer
Explanation

To find the greatest number that leaves the same remainder, calculate the differences between the numbers: 199-166=33, 298-199=99, 298-166=132. The greatest common divisor of 33, 99, and 132 is 33.

AI explanation

Using the property that the greatest number dividing three numbers to leave the same remainder is the HCF of their pairwise differences, find the differences between the numbers. Calculate 199 - 166 = 33 and 298 - 199 = 99. The HCF of 33 and 99 is 33, which is the required greatest number.

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