Question

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

Answer 1

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answer-

We need to find H.C.F of 825, 675 and 450 which would be equal to the longest tape which can measure the three dimensions of the room exactly.

 

Let's find the prime factors of 825, 675 and 450.

 

825 = 3 x 5 x 5 x 11

 

675 = 3 x 3 x3 x 5 x 5

450 = 2 x 3 x 3 x 5x 5

 

 

3, 5 and 5 are the common prime factors.

 

Therefore. H.C.F =3 x 5 x 5=75

 

Therefore, 75 cm is the longest tape which can measure the three dimensions of the room exactly.

Answer 2

Answer:

The length of tape that can measure the three dimensions of the room = HCF of

825,625 and 450

825 = 5²*11*3

675 = 5²*3³

450= 5²*2*3²

Therefore HCF = 5²*3

= 75

The length of the longest tape that can measure the three dimensions of the room exactly = 75cm

Hope it helps you :)