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Question

The length, breadth and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.

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Solution

The given dimensions are 825cm, 675cm & 450cm.
Now to find the length of room we need a common factor of 825,675,450

Using Prime factorization:
825=3×52×11
675=32×52
450=2×32×52

Now from above
HCF=3×52=75
The length of longest rod to measure the length of room is 75cm.

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