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The length, width,and height of a room are 6m 30cm,5m 85cm, 3m 60cm resp. what will the greatest lenght of tape which can measure the dimensions of the rooms in exact number of times?

length  = 6m 30cm = 630 cm

breadth = 5m 85cm = 585 cm

height  = 3m 60 cm = 360 cm

now, 630 = 2 × 3 × 3 × 5 × 7

 585 = 3 × 3 × 5 × 13

 360 = 2 × 2 × 2 × 3 × 3 × 5

so, the HCF of 630, 585 and 360 = 3 × 3 × 5 = 45

so, the greatest length of the tape which can measure the dimensions of the room exact number of times = 45 cm

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Let us convert the length, breadth and height in cm and then find the HCF of the numbers by prime factorization method.

630 cm, 585 cm, 360 cm

now 630 = 7*3*3*5*2, 585 = 5 *13*3*3 , 360= 3*2*2*3*2*5

The HCF of the above numbers = 3*3*5 = 45cm

So the length of the greatest length of tape is 45 cm

Cheers Priya.

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