The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5…

Step-by-Step Solution

To find the greatest number that divides two numbers and leaves specific remainders, follow these steps:

1. Adjust the dividends: Subtract the respective remainders from each number so that they become perfectly divisible by the required number.

   • 1657 - 6 = 1651

   • 2037 - 5 = 2032

2. Find the HCF: The greatest number is the Highest Common Factor (HCF) of these new values (1651 and 2032).

   • Using prime factorization or division method for 1651 and 2032:

   • 1651 = 13 * 127

   • 2032 = 16 * 127

   • The common factor is 127.