Question

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

Answer 1

The longest tape which can measure the length, breadth and height of a room with dimensions $825cm$, $675cm$ and $450cm$ respectively is their H.C.F.

Prime factorization of $825,675$ and $450$ are

$$\begin{gathered} 825=3\times 5\times 5\times 11 \\ 675=3\times 3\times 3\times 5\times 5 \\ 450=2\times 3\times 3\times 5\times 5 \end{gathered}$$

Common factors are $3,5,5$

Therefore, H.C.F of $825,675$ and $450$ is $3\times 5\times 5=75$

Hence, the longest tape which can measure the three dimensions of the room exactly is $75cm$.