The concept of G.C.D/H.C.F is applicable in many real live situations:

Given two containers of capacity 20 litres and 30 litres respectively. Find the capacity of largest jug that can be used to fill each of containers exactly.

Solution  

20= 2x2x5 ,

30= 2x3x5

Common factors are 2 and 5

G.C.D =2X 5= 10