Question

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

Answer 1

$Amountofdieselpresentinthefirst\tan k=403litres$

$Amountofdieselpresentinthesecond\tan k=434litres$

$Amountofdieselpresentinthethird\tan k=465litres$

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 $403$ litres, $434$ litres and $465$ 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.

$Themaximumcapacityofcontainer=H.C.F.of(403,434,465)$

Let us find the prime factorization of $403,434and465$.

$\Rightarrow Factorsof403=13x31$
$\Rightarrow Factorsof434=2x7x31$
$\Rightarrow Factorsof465=3x5x31$

∴ $H.C.Fof(403,434,465)=31$

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