Question

Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in an exact number of times.

Answer 1

- Hint: We will be using the concept of prime factorization of a number to solve the problem. Prime factorization is a method in which we represent a number as a product of prime numbers.

Complete step-by-step solution -

So, we have to find the maximum capacity of a container which can measure 850 litres and 680 litres exactly. To solve the question we will first represent 850 and 680 as prime factorization.
Therefore,
\[\begin{align}
  & 850=2\times 5\times 5\times 17...........\left( 1 \right) \\
 & 680=2\times 2\times 2\times 5\times 17............\left( 2 \right) \\
\end{align}\]
Now to find the maximum capacity of the container we will have to find the highest factor of 850 and 680.
So, from (1) and (2) we can see that the highest common factor is $2\times 5\times 17=170$.
Therefore, 170 litres is the maximum capacity of a container which can measure the petrol of either tanker in an exact number of times.

Note: Alternate method;
We can also solve this question by finding H.C.F of 850 and 680. So, H.C.F of 850 & 650 by long division is,

So, H.C.F of 850 litres and 680 litres is 170. Therefore, the maximum capacity of the container is 170 litres.