If the length, breadth and height of a room are $8 m 25 cm, 6 m 75 cm$ and $4 m 50 cm$

respectively. Then the longest rod which can help measure the three dimensions of the room exactly is ____cm.

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Detailed Solution

If the length, breadth and height of a room are 8m 25cm, 6m 75 cm and 4m 50 cm
respectively. Then the longest rod which can help measure the three dimensions of the room exactly is 75 cm.
Given data,
Length = 8m 25cm
Breadth = 6m 75 cm
Height = 4m 50 cm
Converting the data in cm using 1m=100cm,
Length of the room = 8m 25cm = 825 cm.
Breadth of the room = 6m 75cm = 675 cm.
Height of the room = 4m 50cm = 450 cm.
Finding the prime factors of the length, breadth and height,
825 = 3×5×5×11
675 = 3×3×3×5×5
450 = 2×3×3×5×5
So, the common factors = 3×5×5
Thus, the H.C.F = 75.
Therefore, the required number is 75cm.

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