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

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Detailed Solution

The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively and the longest tape which can measure the three dimensions of the room exactly is 75cm.
It is given that the length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively.
Prime factorization of 825, 675 and 450 are given by,

Question Image

Question Image

Question Image

Question Image

The factors of numbers are,
825: 3 × 5 × 5 × 11
675: 3 × 3 × 3 × 5 × 5
450: 2 × 3 × 3 × 5 × 5
Now, the H.C.F of numbers are,
3 × 5 × 5 = 75 cm.
So, the measurement of the longest tape is 75 cm.

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