Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6…

To find the greatest number that divides two given numbers with specific remainders, you need to adjust the numbers to make them perfectly divisible and then find their Highest Common Factor (H.C.F.).

Step-by-Step Calculation
1. Adjust the numbers:
Subtract the respective remainders from the given numbers to find values that are perfectly divisible by the unknown number.

1657 - 6 = 1651

2037 - 5 = 2032

2. Find the H.C.F. of the adjusted numbers:
We need the H.C.F. of 1651 and 2032.

Using the Euclidean algorithm or prime factorization:

1651 = 13 * 127

2032 = 16 * 127

Both numbers share 127 as a common factor.

3. Identify the result:
The greatest number that divides both adjusted values is 127.