Question
Download Solution PDFThe greatest length of the scale that can measure exactly 30 cm, 90 cm, 1 m 20 cm and 1 m 35 cm lengths is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Lengths that need to be measured exactly: 30 cm, 90 cm, 1 m 20 cm, and 1 m 35 cm.
Formula Used:
Greatest length of the scale = Highest Common Factor (HCF) of given lengths
Calculation:
Convert all lengths to cm:
30 cm
90 cm
1 m 20 cm = 120 cm
1 m 35 cm = 135 cm
Find the HCF of 30, 90, 120, and 135:
Prime Factorization:
30 = 2 × 3 × 5
90 = 2 × 32 × 5
120 = 23 × 3 × 5
135 = 33 × 5
Common factors: 3 and 5
Lowest power of common factors:
31 × 51 = 3 × 5 = 15
The greatest length of the scale that can measure exactly 30 cm, 90 cm, 120 cm, and 135 cm is 15 cm.
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