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 of the room exactly.

Answer 1

The dimensions of room are

Length = 8 m 25 cm = 825 cm

Breadth = 6 m 75 cm = 675 cm

Height = 4 m 50 cm = 450 cm

So the longest rod = HCF of 825, 675 and 450

We know that the prime factorization of $825=3\times 5\times 5\times 11$

The same way prime factorization of $675=3\times 3\times 3\times 5\times 5$

Prime factorization of $450=2\times 3\times 3\times 5\times 5$

So the HCF of 825, 675 and $450=3\times 5\times 5=75$

Therefore, the longest rod which can measure the dimensions of the room exactly is 75 cm.