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The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is_________?

Correct answer: B. 127

  • A. 123
  • B. 127
  • C. 235
  • D. 305

Explanation

Subtract each remainder from its number: 1657 - 6 = 1651 and 2037 - 5 = 2032. The required divisor is GCD(1651, 2032); since 2032 - 1651 = 381, 1651 = 4 x 381 + 127, and 381 = 3 x 127, the GCD is 127. The likely mistake is choosing 123 by subtracting the original numbers or their remainders incorrectly.

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