Question

Three tankers contain $434$ litres, $465$ lites and $403$ lites of fuel respectively. What should be the maximum capacity of a container that can measure the fuel of the three containers exact number of times.

Answer 1

Amount of fuel present in the first tank = $434$ litres

Amount of fuel present in the second tank = $465$ litres

Amount of fuel present in the third tank = $403$ litres

To measure the three tankers, we need to find the container’s maximum measuring capacity. We need to find the HCF because the measuring capacity is smaller than $434$ litres, $465$ litres and $403$ litres.

The Highest Common Factor or HCF is the largest common divisor or GCD of two or more positive integers, as the mathematics rules dictate, appears to be the largest positive integer that divides the numbers without leaving a remainder.

The maximum capacity of container = H.C.F. of $(434,465,403)$

Let us find the prime factorization of $434$, $465$ and $403$.

⇒ Factors of $434=2\times 7\times 31$
⇒ Factors of $465=3\times 5\times 31$
⇒ Factors of $403=13\times 31$

∴ H.C.F of $(434,465,403)=31$

Therefore, $31$ litres of the container is required to measure the quantity. i. e. The maximum measuring capacity is $31$ litres.