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Question
The length, breadth and height of a room are 8m 25cm, 6m 75cm and 4m 50cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
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Solution
Length of the room = 8m 25cm = 825 cmBreadth of the room = 6m 75cm = 675 cmHeight of the room = 4m 50cm = 450 cm
Prime factorization of 825, 675 and 450 are as follows:
825 = 3×5×5×11675 = 3×3×3×5×5450 = 2×3×3×5×5Common factors = 3×5×5H.C.F. = 75Hence, 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.
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.
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