Question

Two tankers contain $850$ litres and $680$ litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker an exact number of times.

Answer 1

We need to find the a number which divides both the numbers an exact number of times, so we need to find the HCF of both the numbers.

Step 1 : Find the HCF of both the numbers

$2$	$850$	$2$	$680$
$5$	$425$	$2$	$340$
$5$	$85$	$2$	$170$
$17$	$17$	$5$	$85$
	$1$	$17$	$17$
			$1$
Prime factors are $850=2\times 5\times 5\times 17$		Prime factors are $680=2\times 2\times 2\times 5\times 17$

So, the HCF of $850and680$ is $2\times 5\times 17=170$

Hence the maximum capacity of a container which can measure the capacity of both the tankers an exact number of times is $170$