Question

Find the greatest number which on dividing 1657 and 2037, leaves remainders 6 and 5, respectively.

• A. 137
• B. 117
• C. 112
• D. 127

Answer 1

Answer:

D. 127

We are given:

• Number divides 1657 leaving remainder 6

• Number divides 2037 leaving remainder 5

  Convert to exact multiples

If divisor is d, then:

• 1657 − 6 = 1651 is divisible by d

• 2037 − 5 = 2032 is divisible by d

So we need:
HCF of 1651 and 2032

Find HCF

Use Euclidean method:

2032 − 1651 = 381

Now:

• HCF(1651, 2032) = HCF(1651, 381)

---

Now divide:

• 1651 ÷ 381 = remainder 127
  So:

• HCF(381, 127)

Now:

• 381 ÷ 127 = remainder 0

So HCF = 127

Final Answer: 127