Question

10. The length, breadth and height of a room are 8m25cm, 6m75cm and 4m50cm
respectively. Determine the longest rod which can measure the three dimensions of the room
exactly,​

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.

Answer 2

Longest rod that can measure the dimensions is the HCF of the three dimensions.

HCF(825,675,450) = 75