Number System — Solve for the missing factor: ? × 48 = 173 × 240. Compute the exact numerical value that must replace the question mark so the equality holds.

Introduction / Context:
This question checks fluency with proportional reasoning and factor manipulation. Instead of multiplying out large numbers on both sides, we isolate the unknown factor by using basic properties of equality and cancellation. This avoids arithmetic overflow and dramatically speeds up the solution.

Given Data / Assumptions:

• An equation: ? × 48 = 173 × 240.
• All quantities are integers; we need the exact value of the missing factor.
• Division by a nonzero number preserves equality and is allowed.

Concept / Approach:
When a product equals another product, we can solve for the unknown by dividing both sides by the known multiplier. Here, dividing both sides by 48 isolates the missing factor. Reducing fractions first avoids large intermediate numbers and keeps the computation clean.

Step-by-Step Solution:
1) Start with ? × 48 = 173 × 240.2) Divide both sides by 48 to isolate ?: ? = (173 × 240) / 48.3) Simplify 240 / 48 = 5 (since 48 × 5 = 240).4) Therefore, ? = 173 × 5 = 865.

Verification / Alternative check:
Compute the right-hand product using the simplified result: 865 × 48 = (800 + 60 + 5) × 48 = 800×48 + 60×48 + 5×48 = 38400 + 2880 + 240 = 41520. Also, 173 × 240 = 173 × (24 × 10) = (173 × 24) × 10 = (4152) × 10 = 41520. Both sides match exactly.

Why Other Options Are Wrong:
545, 685, 495, and 735 each, when multiplied by 48, fail to produce 173 × 240. They deviate by hundreds or thousands once checked against the true product 41520.

Common Pitfalls:
Multiplying 173 × 240 fully before simplifying; forgetting to reduce by 48 early; arithmetic slips when expanding large products; misreading the equation as addition rather than multiplication.

Final Answer:
865