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?

NCERT Math Class 6th Question – 3 Exercise 3.7

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:

The longest tape required to measure the three dimensions of the room = HCF of 825, 675 and 450
Prime factorisations of 825, 675 and 450 are
825 = 3 x 5 x 5 x 11
675 = 3 x 3 x 3 x 5 x 5
450 = 2 x 3 x 3 x 5 x 5

Here, common factors are 3, 5 (two times).
∴ HCF of 825, 675 and 450 = 3 x 5 x 5 = 75
Hence, the required longest tape = 75 cm.