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.

Here we are given that the length of a room is 825 cm

The breadth of a room is 675 cm

The height of a room is 450 cm

Using the prime factorization method, we will find prime factors of 825, 675, and 450.

825 = 3 × 5 × 5 × 11

675 = 3 × 3 × 3 × 5 × 5

450 = 2 × 3 × 3 × 5 × 5

HCF = 3 × 5 × 5 = 75 cm

The longest tape, which can measure the room's three dimensions, is 75 cm long.