Question

The the length, breadth and height of a room are 8 metre 25 cm 6 m 75 cm and 4 m 50 cm respectively find the length of the longest rod that can measure the three dimension of the room exactly

Answer 1

Length of the room = 8.25 m = 8.25 *100=825 cm
Breadth of the room = 6.75 m = 6.75 *100=675 cm
Height of the room = 4.50 m = 4.50 *100=450  cm
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.