Two water tanks contain 250 and 400 litres of water res

SOLUTION

To find the maximum capacity of a bucket that can exactly measure the water in the two tanks, we have to find the HCF of 250 and 400.

Using prime factorisation method,

$\begin{array}{cc}5& 250\\ 5& 50\\ 5& 10\\ 2& 2\\ & 1\end{array}$

 $250=5\times 5\times 5\times 2$

$\begin{array}{cc}5& 400\\ 5& 80\\ 2& 16\\ 2& 8\\ 2& 4\\ 2& 2\\ & 1\end{array}$
 $400=5\times 5\times 2\times 2\times 2\times 2$

So,

$250=5\times 5\times 5\times 2$

$400=5\times 5\times 2\times 2\times 2\times 2$

HCF of 250 and 400
$=5\times 5\times 2=50$

Therefore, a 50 litre bucket has to be used to measure 250 and 400 litres of water exactly.

Note:
To measure 250 l we measure 5 times as 50 x 5 = 250
To measure 400 l we measure 8 times as 50 x 8 = 400