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.

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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.

Updated on 10-Oct-2022 13:30:51