The length, breadth and height of a room are 8 m and 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.
To find the length of largest rod, we should find HCF of 8m and 25 cm, 6 m 75 cm and 4 m 50 cm
Length = 825 cm; Breadth = 675 cm; Height = 450 cm
Prime factors of 825 = 3 × 5 × 5 × 11
Prime factors of 675 = 3 × 3 × 3 × 5 × 5
Prime factors of 450 = 2 × 3 × 3 × 5 × 5
Therefore HCF of 825, 675 and 450 is: 3 × 5 × 5 = 75
Hence, the length of rod is: 75 cm