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.
-
A31 cm
-
B29 cm
-
C28 cm
-
D32 cm
-
E27 cm
Answer
Correct Answer: 31 cm
Explanation
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 cmVerification / 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