Question

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

Answer 1

Given:

Length of the room = 8 m 25 cm = 825 cm
Breadth of the room = 6 m 75 cm = 675 cm
Height of the room = 4 m 50 cm = 450 cm

The longest rod will be given by the HCF of 825, 675 and 450.
Prime factorisation of 825 = 3 × 5 × 5 × 11
Prime factorisation of 675 = 3 × 3 × 3 × 5 × 5
Prime factorisation of 450 = 2 × 3 × 3 × 5 × 5
Therefore, HCF of 825, 675 and 450 = 3 × 5 × 5 = 75

Thus, the required length of the longest rod is 75 cm.