Question
Download Solution PDFFind the highest length which can be used to measure exactly the lengths 48 m, 72 m, 96 m and 120 m.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Lengths to measure = 48 m, 72 m, 96 m, and 120 m
Formula Used:
To find the highest length that can measure these lengths exactly, we calculate their Highest Common Factor (HCF).
Calculation:
Find the HCF of 48, 72, 96, and 120:
Prime factorization:
48 = 24 × 3
72 = 23 × 32
96 = 25 × 3
120 = 23 × 3 × 5
Common prime factors: 2 and 3
Lowest powers of common factors:
23
3
HCF = 23 × 3
⇒ HCF = 8 × 3
⇒ HCF = 24
The highest length that can measure 48 m, 72 m, 96 m, and 120 m exactly is 24 m.
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