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Lengths of two iron rods are $$144\ \text{m}$$ and $$64\ \text{m}$$. Which of the following is the maximum length of the rod which can measure each of them completely?
The required length is the HCF of 144 and 64. Since $$144 = 2^4 \times 3^2$$ and $$64 = 2^6$$, the HCF is $$2^4 = 16$$. So a rod of $$16\ \text{m}$$ can measure both exactly.
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