Question

Two tankers contain $500$ and $600$ liters of milk respectively. Find the maximum capacity of a container which can measure the milk of each container when used an exact number of times.

Answer 1

Two tankers contain $500$ and $600$ liters of milk

Now, to measure the milk in exact number of times, take the H.C.F. of $500$ and $600$

Prime factorizations of $500$ and $600$ are:-

$500=2\times 2\times 2\times 3\times 5\times 5=2^3\times 3\times 5^2$

$600=2\times 2\times 5\times 5\times 5=2^2\times 5^3$

H.C.F $=2^2\times 5^2=100$

$\therefore$ the maximum capacity of a container which can measure the milk of each container when used an exact number of times is $100$ liters