When 2468 is divided by 37, what remainder is obtained?

Introduction / Context:
This is a straightforward remainder problem in basic arithmetic and number theory. It checks comfort with long division or modular arithmetic, which is an essential skill for many quantitative aptitude questions.

Given Data / Assumptions:
- Dividend: 2468.
- Divisor: 37.
- We must find the remainder when 2468 is divided by 37.

Concept / Approach:
The remainder r in dividing a number N by d is defined as the difference N − d * q, where q is the integer quotient floor(N ÷ d). We can either perform standard long division or use approximate multiplication to find q and then compute the remainder. The idea is to identify the largest multiple of 37 that does not exceed 2468.

Step-by-Step Solution:
Start with N = 2468 and d = 37. Compute 37 × 60 = 2220. Increase the multiple: 37 × 66 = 2442. Try 37 × 67 = 2479, which is greater than 2468, so 67 is too large. Thus the greatest integer quotient q is 66 and the remainder is 2468 − 2442 = 26.

Verification / Alternative Check:
We can confirm by direct division: 2468 ÷ 37 is approximately 66.7, so the integer part is 66. Recomputing 37 × 66 = 2442 and subtracting from 2468 gives 26. Since 0 ≤ remainder < 37, and 26 is in this range, the value is consistent.

Why Other Options Are Wrong:
36 is too close to 37 and would imply the dividend is just one less than the next multiple of 37, which is not true here.
18 and 14 are smaller remainders that do not match the calculation 2468 − 2442 = 26.
10 is also not obtained in any correct computation of 2468 mod 37.

Common Pitfalls:
A common error is miscalculating intermediate products such as 37 × 66, which leads to an incorrect remainder. Some learners may also incorrectly round rather than floor the quotient and then adjust, which is wrong in modular arithmetic. Careful and systematic multiplication avoids these mistakes.

Final Answer:
The remainder when 2468 is divided by 37 is 26.