Question

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.

Answer 1

$\text{The measurement of longest tape = H.C.F of 825 cm, 675 cm and 450cm.}$



$\text{Factors of 825 = 3 x 5 x 5 x 11 }$



$\text{Factors of 675 = 3 x 5 x 5 x 3 x 3 }$



$\text{Factors of 450 = 2 x 3 x 3 x 5 x 5 }$



$\text{H.C.F = 3 x 5 x 5 = 75 cm }$



$\textbf{Therefore, the longest tape is 75 cm.}$