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

**Solution:**

We will use the concept of the HCF(Highest Common Factor) to solve this.

To determine the longest tape required to measure the three dimensions of the room, we need to calculate the HCF of the given dimensions that are 825, 675, and 450.

Prime factorization of 825, 675, and 450 can be calculated by finding prime factors.

Prime factorization of 825 = 3 × 5 × 5 × 11

Prime factorization of 675 = 3 × 3 × 3 × 5 × 5

Prime factorization of 450 = 2 × 3 × 3 × 5 × 5

Let us try to find the highest common factor.

Here we observe that 3 × 5 × 5 is the highest common factor.

Hence HCF of 825, 675, and 450 is 75.

Thus, the length of the longest tape required to measure the three dimensions of the room will be 75 cm.

You can also use the HCF Calculator to answer this.

NCERT Solutions Class 6 Maths Chapter 3 Exercise 3.7 Question 3

## The length, breadth and height of a room are 825 cm, 675 cm and 450 cm respectively. Find the longest tape which can measure the three dimensions of the room e×actly.

**Summary:**

If the length, breadth, and height of a room are 825 cm, 675 cm, and 450 cm respectively, the length of the longest tape required to measure the three dimensions of the room will be 75 cm.