Question

The length , breadth and height of a room are 14m 85cm , 9m 30cm, and 7m 5cm respectively . what is the length of the longest rod which can measure the dimensions of the room exactly.​

Answer 1

Answer:

Step-by-step explanation:

Length of the room = 14.85 m or 1485 cm,

Breadth of the room = 9.30 m = 930 cm,

Height of the room = 7.05 m = 705 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 1485,930,705.

Prime factorization of 1485 =  3*3*3*5* 11,

Prime factorization of 930 = 2*3*5*31,

Prime factorization = 705= 3*5*47

Common factors = 3*5*5,

H.C.F. = 75

Hence, H.C.F. of 1485,930,705 is 75

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

Answer 2

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