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Q.7 Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.

Answer :

Maximum capacity of the required measure is equal to the HCF of 403, 434 and 465.
$$\begin{array}{|l} \llap{13~~~~} 403 \\ \hline \llap{31~~~~} 31 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 434 \\ \hline \llap{7~~~~} 217 \\ \hline \llap{31~~~~} 31 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 465 \\ \hline \llap{5~~~~} 155 \\ \hline \llap{31~~~~} 31 \\ \hline 1 \end{array}$$ 403=13× 31
434 = 2 × 7 × 31
465 = 3 × 5 × 31
HCF = 31
Hence, the maximum capacity of the required container = 31 litres.