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

__Given__:

Length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively.

__To find__:

We have to find the longest tape which can measure the three dimensions.

__Solution__:

To find the longest tape which can measure the three dimensions of the room exactly we need to calculate HCF of 825, 675 and 450.

__Calculating HCF of 825, 675 and 450__:

Writing all of the numbers as a product of their prime factors:

The prime factorisation of 825 is:

- $825 = 3 \times 5 \times 5 \times 11$

The prime factorisation of 675 is:

- $675 = 3 \times 3 \times 3 \times 5 \times 5$

The prime factorisation of 450 is:

- $450 = 2 \times 3 \times 3 \times 5 \times 5$

HCF of 825, 675 and 450 $=3\times5\times5=75$

So,

HCF (825, 675, 450) = 75

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

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