Find the greatest measuring length: Determine the greatest possible length (in centimeters) that measures exactly 4 m 3 cm, 4 m 34 cm, and 4 m 65 cm.

Introduction / Context:
“Measuring exactly” multiple lengths using the greatest possible length is a Highest Common Factor (HCF) problem. Converting all measures to the same unit (centimeters) and computing the HCF yields the required maximum measuring length.

Given Data / Assumptions:

• Lengths: 4 m 3 cm, 4 m 34 cm, 4 m 65 cm.
• 1 m = 100 cm.

Concept / Approach:
Convert each to centimeters and compute their HCF. The HCF is the largest length that divides all three exactly with no remainder.

Step-by-Step Solution:

Verification / Alternative check:
Divide each: 403/31 = 13, 434/31 = 14, 465/31 = 15 — all integers.

Why Other Options Are Wrong:
28, 29, 32, and 27 do not divide all three lengths exactly (at least one will leave a remainder).

Common Pitfalls:
Forgetting to convert meters to centimeters consistently; attempting to take the HCF in mixed units leads to errors.

Final Answer:
31 cm