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 cmBreadth of the room = 6m 75cm = 675 cmHeight of the room = 4m 50cm = 450 cmPrime factorization of 825, 675 and 450 are as follows:825 = 3×5×5×11675 = 3×3×3×5×5450 = 2×3×3×5×5 Common factors = 3×5×5H.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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