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Question

The length, breadth and height of a room are $$825$$cm, $$675$$cm and $$450$$cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

Solution
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Length$$=825$$cm $$=3\times 5\times 5\times 11$$
Breadth$$=675$$cm $$=3\times 3\times 3\times 5\times 5$$
Height$$=450$$cm $$=2\times 3\times 3\times 5\times 5$$
Longest tape$$=$$HCF of $$825, 675$$ and $$450=3\times 5\times 5=75$$cm
Therefore, the longest tape is $$75$$cm.

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