The greatest number, which divides 2248 and 1761 to leave 3 and 1 respectively as remainders, is:

Correct option is B

Given:

The greatest number that divides 2248 and 1761, leaving remainders of 3 and 1, respectively.

Solution:

Subtract the remainders from the given numbers:

2248 − 3 = 2245, 1761 − 1 = 1760

Prime factorization of 2245:

2245 = 5 × 449 (449 is a prime number)

Prime factorization of 1760:

1760 = 2⁵ × 5 × 11

The common prime factor is 5, with the lowest power being 5¹

Therefore, HCF (2245, 1760) = 5.

Thus, the greatest number that divides 2248 and 1761 to leave remainders of 3 and 1, respectively, is 5