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Question

The length, breadth and height of a room are $$8$$m $$25$$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.


Solution

Length of the room = 8m 25cm = 825 cm
Breadth of the room = 6m 75cm = 675 cm
Height of the room = 4m 50cm = 450 cm

Prime factorization of 825, 675 and 450 are as follows:

825 = 3×5×5×11
675 = 3×3×3×5×5
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.

Therefore the length of the longest tap is 75 cm which can measure the three dimensions of the room exactly.

Maths

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