Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6…
20252024
Find the greatest number, which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively.
Answer: A. 127 — 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…
- A.
127
- B.
132
- C.
114
- D.
108
Attempted by 3 students.
Show answer & explanation
Correct answer: A
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.