Question

The length, breadth and height of a room are 8 m 25cm, 6m 75cm and 4m 50 cm respectively. Determine the longest rod which can measure the three dimensions of the room exactly.

Answer 1

We have,
8 m 25cm = 825cm,
6m 75cm = 675cm
4 m 50 cm = 450 cm
Length of the longest rod in cm is the HCF of 825, 675 and 450.
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
HCF (825, 675 and 450) = 3 $\times$ 5 $\times$ 5 = 75
Hence, the required length of rod = 75 cm