The length, breadth and height of a room are 6 m 30 cm, 5 m 85 cm and 3 m 60 cm, respectively. Determine the longest rod which can measure the three dimensions of the room exactly.
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Answer:
First of all we will take the HCF of all but, before that we will convert them in a similar unit :
6m 30cm =6 X 100 + 30
=630cm
5m 85cm =5 X 100 + 85
=585cm
3m 60cm =3 X 100 + 60
=360cm
Now, lets take the HCF :
HCF of 630cm, 585cm, 360cm
= 45 cm
Step-by-step explanation:
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Step-by-step explanation:
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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