Multiple choice

The greatest number which on dividing $1657$ and $2037$ leaves remainders $6$ and $5$ respectively, is:

  1. $123$
  2. $127$
  3. $235$
  4. $305$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The number must divide (1657 - 6) = 1651 and (2037 - 5) = 2032. Find GCD(1651, 2032). 1651 = 13 * 127. 2032 = 16 * 127. GCD is 127.

AI explanation

Subtract the remainders from the respective numbers to get 1651 and 2032. The required number is the highest common factor of 1651 and 2032. By Euclid's algorithm or prime factorization, the HCF is 127. The greatest number is 127.

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