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Question
Two ropes, one 8 meters long and the other 12 meters long are to be cut into pieces of the same length. What will the maximum possible length of each piece be?
Solution
Length of one rope = 8 m
Length of other rope = 12 m
The maximum possible length of each piece of rope of the same length that can be cut from the two given ropes is the HCF of 8 m and 12 m.
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
Common factors of 8 and 12: 1, 2, 4
HCF of 8 and 12 = 4
∴ Maximum possible length of each piece of rope of same length = 4 m
Thus, the maximum possible length of each piece of rope is 4 m.
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