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Question

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

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Solution

The dimensions of room are

Length = 8 m 25 cm = 825 cm

Breadth = 6 m 75 cm = 675 cm

Height = 4 m 50 cm = 450 cm

So the longest rod = HCF of 825, 675 and 450

We know that the prime factorization of 825=3×5×5×11

The same way prime factorization of 675=3×3×3×5×5

Prime factorization of 450=2×3×3×5×5

So the HCF of 825, 675 and 450=3×5×5=75

Therefore, the longest rod which can measure the dimensions of the room exactly is 75 cm.

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