Question

the length ,breath and height of a room are

Answer 1

Length of the room = 8.25 m or 825 cm

Breadth of the room = 6.75 m = 675 cm

Height of the room = 4.50 m = 450 cm

We have to find the longest rod that can measure the three dimensions of the room exactly. For this, we have to find the Highest Common Factor of 825, 675 and 450.

Prime factorization of 825 = 3*5*5*11

Prime factorization of 675 = 3*3*3*5*5

Prime factorization = 450 = 2*3*3*5*5

Common factors = 3*5*5

H.C.F. = 75

Hence, H.C.F. of 825, 675 and 450 is 75

The length of the longest rod is 75 cm which can measure the three dimensions of the room exactly.