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.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: Convert: 4 m 3 cm = 403 cm; 4 m 34 cm = 434 cm; 4 m 65 cm = 465 cmHCF(403, 434): 434 − 403 = 31; and 403 = 31 × 13 ⇒ HCF = 31Now HCF(31, 465): 465 = 31 × 15 ⇒ HCF remains 31Therefore, the greatest measuring length is 31 cm 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

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.

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