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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.


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Solution

Amountofdieselpresentinthefirsttank=403litres

Amountofdieselpresentinthesecondtank=434litres

Amountofdieselpresentinthethirdtank=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.

Factorsof403=13x31
Factorsof434=2x7x31
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.


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