What is the quotient obtained when 7251 is divided by 66?

Introduction / Context:
This question is a direct test of division skills, focused on finding the integer quotient when one number is divided by another. It reinforces basic arithmetic operations that underpin many more complex quantitative problems.

Given Data / Assumptions:
- Dividend: 7251.
- Divisor: 66.
- We are asked for the quotient, which is the integer part of 7251 ÷ 66.

Concept / Approach:
To find the quotient q and remainder r when N is divided by d, we write N = d * q + r, where 0 ≤ r < d. Here we only need q. Performing long division or approximating the quotient and refining it will give the correct integer value.

Step-by-Step Solution:
Let N = 7251 and d = 66. Approximate: 66 × 100 = 6600, which is less than 7251. Increase the multiple: 66 × 110 = 7260, which is slightly greater than 7251. Therefore the quotient must be just below 110, so try 66 × 109. Compute 66 × 109 = 66 × (100 + 9) = 6600 + 594 = 7194, which is less than 7251.

Verification / Alternative Check:
After computing 66 × 109 = 7194, we can find the remainder as 7251 − 7194 = 57. Because 57 is less than 66, the division is consistent with quotient 109 and remainder 57. If we tried quotient 110, the product 66 × 110 = 7260 would exceed 7251, which is not allowed. Therefore, the correct integer quotient is 109.

Why Other Options Are Wrong:
110 would give a product greater than the dividend, which is impossible for a valid quotient.
111 and 112 are even larger and would lead to products further above 7251.
108 gives 66 × 108 = 7128, which is less than 7194 and thus not the greatest integer quotient; the actual quotient is higher at 109.

Common Pitfalls:
A common error is to stop at an approximate estimate such as 110 without checking whether the product exceeds the dividend. Another mistake is miscalculating 66 × 109 or similar products. Careful multiplication and a quick check that the product does not exceed the dividend ensure the correct quotient is chosen.

Final Answer:
The quotient when 7251 is divided by 66 is 109.