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Factors of 825 are 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275 and 825.
Factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225 and 675.
Factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225 and 450.
∴ Common factors of 825, 675 and 450 are 1, 3, 5, 15, 25 and 75.
Highest of these common factors is 75.
Hence, the length of the longest tape which can measure the three dimensions of the room exactly is 75cm.
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