Question

The length,breadth and hieght of a room are 7m 25cm , 9m 25 cm ans 8m 25cm respectively. Determine the length of the largest tape which can measure the three dimensions of the room exactly

Answer 1

Answer:

Length of the room = 8m 25cm = 825 cm

Breadth of the room = 6m 75cm = 675 cm

Height of the room = 4m 50cm = 450 cm

Prime factorization of 825, 675 and 450 are as follows:

825 = 3×5×5×11

675 = 3×3×3×5×5

450 = 2×3×3×5×5

Common factors = 3×5×5

H.C.F. = 75

Hence, H.C.F. of 825, 675 and 450 is 75.

Therefore the length of the longest tap is 75 cm which can measure the three dimensions of the room exactly.

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Answer 2

Answer:

25cm

Step-by-step explanation:

length of the room =  7m 25 cm = 725cm

breadth of the room= 9m 25cm  = 925cm

height of the room   = 8m 25cm = 825cm

GCD of these 3 dimensions will give you the length of the largest tape which measures them exactly.

factors of 725 are: 1, 5, 25, 29, 145, 725

factors of 825 are: 1, 3, 5, 11, 15, 25, 33, 55, 75, 165, 275, 825

factors of 925 are: 1, 5, 25, 37, 185, 925

Then the greatest common divisor is 25.

and hence the measure of the largest tape is 25cm