The length , breadth and height of a room are 300cm, 175cm and 500m respectively. Find the longest tape which can measure the dimensions of the room exactly.
Answers
Given:
The length, breadth and height of a room are 300cm, 175cm and 500m respectively
To find:
The longest tape which can measure the dimensions of the room exactly.
Solution:
(1). To find the length of the longest tape that can measure the dimensions of the room exactly, we will find the H.C.F. of 300 cm, 175 cm & 500 cm.
(2). Now to find the H.C.F. we will use the prime factorisation method which is as follows:
Factors:
300 = 2 × 2 × 3 × 5 × 5
175 = 5 × 5 × 7
500 = 2 × 2 × 5 × 5 × 5
H.C.F.
∴ H.C.F. of 300, 175 & 500 = 5 × 5 = 25
Thus, the length of the longest tape which can measure the dimensions of the room exactly is → 25 cm.
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