There are three heaps of rice weighing 120 kg, 144 kg and 204 kg. Find the maximum capacity of a bag so that the rice of each heap can be packed in exact number of bags.

The required maximum capacity of a bag is the HCF of 120, 144 and 204.

First, find HCF of 120 and 144:

$\begin{array}{l} 120\overline{\smash{\big)}144\smash{\big(}}\phantom{}1 \ \phantom{x}\phantom{))}\underline{-120} \ \phantom{{x^2 } 1())}24\overline{\smash{\big)}120\smash{\big(}}\phantom{}5 \ \phantom{{x} +1xa}\underline{-120} \ \phantom{{x^2 a} + 2x+} 0 \ \end{array}$

So, HCF of 120 and 144 = 24.

Now, find HCF of 24 and 204:

$\begin{array}{l} 24\overline{\smash{\big)}204\smash{\big(}}\phantom{}8 \ \phantom{x}\phantom{}\underline{-192} \ \phantom{{x^2 } 1)}12\overline{\smash{\big)}24\smash{\big(}}\phantom{)}2 \ \phantom{{x} +1)}\underline{-24} \ \phantom{{x^2 a} + 2x} 0 \ \end{array}$

So, HCF of 24 and 204 = 12.

Hence, the maximum capacity of a bag is 12 kg.