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# Q.3 The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

$$\begin{array}{|l} \llap{3~~~~} 825 \\ \hline \llap{5~~~~} 275 \\ \hline \llap{5~~~~} 55 \\ \hline \llap{11~~~~} 11 \\ \hline 1 \end{array}$$ $$\begin{array}{|l} \llap{3~~~~} 675 \\ \hline \llap{3~~~~} 225 \\ \hline \llap{3~~~~} 75 \\ \hline \llap{5~~~~} 25 \\ \hline \llap{5~~~~} 5 \\ \hline 3 \end{array}$$ $$\begin{array}{|l} \llap{2~~~~} 450 \\ \hline \llap{3~~~~} 225 \\ \hline \llap{3~~~~} 75 \\ \hline \llap{5~~~~} 25 \\ \hline \llap{5~~~~} 5 \\ \hline 3 \end{array}$$ 825 = 3 x 5 x 5 x 11