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 three containers an exact number of times.

Answer 1

Hint: As it is written in the question that we have to find the maximum capacity of a container then we can think about finding the H.C.F. It can be a good approach to solve this question. Also, it is asking about all the three containers then there can be something common between them.

Complete step-by-step answer:
In the given solution,
To find the maximum capacity of the container that can measure the diesel of three tankers we have to take their H.C.F.
H.C.F is the product of all the factors which are common in all the numbers.
So,
$Factors\,of\,403\, = \,1,13,31,403$
$Factors\,of\,434\, = \,1,2,7,14,31,62,217,434.$
$Factors\,of\,465\, = \,1,3,5,15,31,93,155,465.$
Therefore, the factors which are common in all the three numbers are $1\,and\,31.$
So, the highest common factor of $403,\,434\,and\,465\, = \,31 \times 1 = 31$.
Hence, the maximum capacity of the container should be $31\, litres.$

Note: The Highest Common Factor of two numbers is the highest possible number which divides both the numbers exactly. HCF of a and b is denoted by HCF (a, b). let d be the HCF (a, b), then you can’t find the common factor of a and b greater than the number d. The highest common factor (HCF) is also called the greatest common divisor (GCD).