CDS 2026 (I) Elementary Mathematics, question 24

Topic: HCF and LCM

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Q24

Let NN be the greatest number that will divide 600600, 631631 and 724724, leaving the same remainder. What is the value of NN ?

  1. (a) 4141
  2. (b) 3737
  3. (c) 3333
  4. (d) 3131Correct answer

Solution.

Answer: (d) 3131

  1. Equal remainders mean the divisor must divide every pairwise difference.
  2. The differences 631−600=31631 - 600 = 31 and 724−631=93724 - 631 = 93 have HCF 31.
  3. All three numbers leave remainder 11 on division by 31, confirming the condition.