Math, asked by sangeetavinod04, 1 year ago

solve the problem plz ​

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Answered by BrainlySmile
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Answer- The above question is from the chapter 'Real Numbers'.

The question is an applicative one.

A merchant has 3 kinds of oil i.e. 120 litres, 180 litres and 240 litres. He wants to put them in a container which can hold the greatest capacity of oil.

Clearly, the tin should hold even the least kind of oil available.

HCF(120, 180, 240) = Greatest capacity of tin to hold 3 kinds of oil.

← H.C.F. 120, 180, 240

Thus, we will find the HCF of 120, 180 and 240 by prime factorisation method.

120 = 2 × 2 × 2 × 2 × 3 × 5 = 2⁴ × 3 × 5

180 = 2 × 2 × 3 × 3 × 5 = 2² × 3² × 5

240 = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 2⁵ × 3 × 5

HCF(120, 180, 240) = 2² × 3 × 5 = 60 litres

∴ Greatest capacity of tin = 60 litres.

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