Question

the length breath and height of a room are 1050 cm,750,and 425 respectively find the length of longest tape which can measure the three dimensions of the room exactly​

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The length, breadth and height of a room are 1050cm, 750cm and 425cm respectively. Find the length of the longest tape which can measure the three dimensions of the room exactly.

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ANSWER

The length, breadth and height of a room are 1050cm, 750cm and 425cm respectively.

To measure these length we need tape which is of length of common factor of all three lengths.

To find length of longest tape for measuring all three room dimensions exactly we have to find HCF of three numbers.

First we have to convert these numbers into prime factors.

So,

1050=21×50=7×3×2×5=2×3×5

2

×7

750=25×30=2×3×5

3

425=25×17=5

2

×17

So, common among these factors is 5

2

So, HCF=5

2

=25

So, longest tape which can measure all three given lengths exactly is 25 cm