Question

There are three tankers containing 294 L. 252 L. 210 L of petrol respectively Find
the maximum capacity of a container which can measure the petrol of all the three
tankers when used an exact number of times​

Answer 1

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

The question is an applicative one.

Given question: There are three tankers containing 294 L , 252 L and 210 L of petrol respectively. Find the maximum capacity of a container which can measure the petrol of all the three tankers when used an exact number of times​.

Solution: A person has 3 different quantities of petrol i.e. 294 litres, 252 litres and 210 litres.

He wants to put them in a container which can measure the greatest capacity of petrol.

Clearly, the container should hold even the least quantity of petrol available.

HCF(294, 252, 210) = Greatest capacity of container to hold 3 quantities of petrol.

← H.C.F. 294, 252, 210

Thus, we will find the HCF of 294, 252 and 210 by prime factorisation method.

294 = 2 x 3 x 7 x 7 = 2 × 3 × 7²

252 = 2 x 2 x 3 x 3 x 7 = 2² × 3² × 7

210 = 2 x 3 x 5 x 7

HCF(294, 252, 210) = 2 × 3 × 7 = 42 litres

∴ Greatest capacity of container = 42 litres.