Question

The length breadth and height of a room are 825 cm 675 cm and 450 cm respectively find the length of the longest rod that can measure the three dimensions of the room exactly

Answer 1

Answer:

$\begin{tabular}{l|r}3&825\\\cline{1-2}5&275\\\cline{1-2}5&55\\\cline{1-2}11&11\\\cline{1-2}&1\end{tabular}\qquad\begin{tabular}{l|r}3&675\\\cline{1-2}3&225\\\cline{1-2}3&75\\\cline{1-2}5&25\\\cline{1-2}&5\end{tabular}\qquad\begin{tabular}{l|r}2&450\\\cline{1-2}3&225\\\cline{1-2}3&75\\\cline{1-2}5&25\\\cline{1-2}&5\end{tabular}$

$\rule{170}{1}$

$\star\:\:\sf 825=\it{3\times5\times5} \:\sf\times\:5\times11\\\star\:\:\sf675=3\times3\times\it3\times5\times5\\\star\:\:\sf450=2\times3\times3\times\it3\times5\times5 \\\\\\\begin{aligned}\bf{\dag}\:\:\sf HCF(825,675,450)=3 \times 5 \times 5\\\sf = 75\:cm\:\:\quad\end{aligned}$

⠀

$\therefore\:\underline{\textsf{Longest rod that can fit the room is \textbf{75 cm}}.}$