Question

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.

Answer 1

HCF of two or more number is the highest number which divides the given numbers exactly.
The measurement of longest tape = HCF of 825 cm, 675 cm, and 450 cm.
Factors of 825 = $3\times 5\times 5\times 11$
Factors of 675 = $3\times 5\times 5\times 3\times 3$
Factors of 450 = $2\times 3\times 3\times 5\times 5$
HCF = $3\times 5\times 5=75cm$
Therefore, the longest tape which can measure the three dimensions of the room exactly is 75 cm.