Reverse a product to find the missing factor: Find the number that satisfies ? × 147 = 6909.

Introduction / Context: Another single-step multiplication equation: recover the unknown integer by dividing the product by the known factor. Efficient estimation narrows the candidate before confirming exactly.

Given Data / Assumptions:

• Known factor: 147.
• Product: 6909.
• We seek q = 6909 / 147.

Concept / Approach: Approximate: 147 × 50 = 7350, which is too high. Reduce by 3 × 147 = 441 to test 47: 7350 − 441 = 6909. This mental adjustment confirms the exact multiplier without long division.

Step-by-Step Solution:Compute 147 × 50 = 7350.Subtract 3 × 147 = 441 to try 47: 7350 − 441 = 6909.Thus q = 47.

Verification / Alternative check: Direct division gives 6909 ÷ 147 = 47 exactly, validating the mental adjustment approach.

Why Other Options Are Wrong:37 and 27 yield products far below 6909; 67 overshoots substantially. Only 47 matches the target.

Common Pitfalls: Estimating 147 as 150 and then failing to correct; not adjusting by the proper multiple when stepping down from 50 to the correct factor.

Final Answer: 47