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Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same?

Correct answer: D. 106

  • A. 53
  • B. 112
  • C. 108
  • D. 106

Explanation

If the remainders are equal, the greatest divisor must divide the differences between the numbers. The differences are 909 - 697 = 212 and 1227 - 909 = 318, and gcd(212, 318) = 106, so the required number is 106. The likely mistake is option b, 112, which does not divide both differences.

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