Foundation
Mathematics Foundation
HCF and LCM
Properties of Real Number
Ratio Proportion
Question
Three ropes are 7m,12m 95cm and 3m 85 cm long. What is the greatest possible length that can be used to measure these ropes?
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Solution
The given three ropes are 7m, 12 m 95cm and 3m85cm long. We know that 1m = 100cm, therefore,
The length of the respective ropes will be:
1st rope 7 × 100 = 700cm
2nd rope (12 × 100) + 95 = 1200 + 95 = 1295cm
3rd rope = (3 × 100) + 85 = 300 + 85 = 385cm
Now, let us factorize the length of the ropes as follows:
700 = 2 × 2 × 5 × 5 × 7
1295 = 5 × 7 × 37
385 = 5 × 7 × 11
The highest common factor (HCF) is 5 × 7 = 35
Hence, the greatest possible length that can be used to measure these ropes is 35cm.