Question

Two tankers contain \[850\] litres and \[680\] litres of kerosene oil respectively, then the maximum capacity of a container which can measure the kerosene out of both the tankers when used an exact number of times is __________.
A) \[170\] litres
B) \[85\] litres
C) \[34\] litres
D) \[10\] litres

Answer 1

Hint: We have to find the maximum capacity of a container which can measure the kerosene out of both the tankers. For that, we have to find the highest coefficient factor of \[850\] and \[680\] by prime factorization method. We will factorize \[850\] and \[680\] into their simplest terms and then take the common terms.

Complete step-by-step answer:
It is given that: Two tankers contain \[850\] litres and \[680\] litres of kerosene oil respectively.
We have to find the maximum capacity of a container which can measure the kerosene out of both the tankers.
To find the maximum capacity of a container which can measure the kerosene out of both the tankers, we have to find the highest coefficient factor of \[850\] and \[680\] by prime factorization method.
First, we will factorize \[850\] and \[680\].
We get,
\[850 = 2 \times 5 \times 5 \times 17\] and,
\[680 = 2 \times 2 \times 2 \times 5 \times 17\]
Taking the common terms, we get, HCF of \[850\] and \[680\]\[ = 17 \times 2 \times 5 = 170\]
Hence, the maximum capacity of a container which can measure the kerosene out of both the tankers when used an exact number of times is \[170\] litres.

$\therefore $ The correct option is A) \[170\] litres.

Note: We already know that the greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor. It is also called the Greatest Common Measure (GCM) and Greatest Common Divisor (GCD).
Since, we have to find the maximum capacity of the container and by the definition of HCF, we get the greatest number. So, we apply HCF formula.
We can factorize the given by another way of method,
Now we are going use prime factorization of tree method,

Hence, HCF of \[850\] and \[680\]\[ = 17 \times 2 \times 5 = 170\]
$\therefore $ The correct option is A) \[170\] litres.