Question

Three tankers contain 403 litres, 434 litres and 465 litres of diesel respectively. Find the maximum capacity of a container that can measure the diesel of the three containers exact number of times.

Answer 1

Hint: Take the HCF of the three tankers to find the maximum capacity. Out of the HCF of 403, 434 and 465, find the common factor in all 3 HCF. Compare them and find the maximum capacity.

Complete step-by-step answer:
Amount of diesel present in the first tank = 403 litres

Similarly the amount of diesel present in the 2nd tank = 4234 litres

The amount of diesel present in the 3rd tank = 465 litres

We need to find the maximum measuring capacity of the container to measure the three tankers. Since measuring capacity is smaller than 403, 434, 465, we need to find the HCF.

Thus max measuring capacity = HCF (403, 434, 465)

We can find HCF by using the prime factorization method. Prime factorization is finding which prime numbers multiply together to make the original number.

A prime number is a number greater than 1 that cannot be made into a whole number. For a prime number the only factors are 1 and the number itself.

Now let us find the prime factorization of 403, 434 and 465.
\[\begin{align}
  & 403=1\times 13\times 31 \\
 & 434=1\times 2\times 7\times 31 \\
 & 465=1\times 3\times 5\times 31 \\
\end{align}\]

From the above, we can say that 31 is common for 403, 434 and 465.
\[\therefore HCF(403,434,465)=31\]
\[\therefore \]HCF is 31.
Thus we got the maximum measuring capacity as 31 litres.

Note:
We can also find the maximum measuring capacity by long division method.
The quotient will give the maximum measuring capacity.