First the base has to be at least 5, due to the presence of 4.

40/20 = 2 in all bases, but since 20>14 the integer value must be greater than 2.

44/11 = 4 in all bases but since 11<14 the integer value must be less than 4.

That means 41/14 = 3 for the fraction to be an integer.

Base 10: 14*3 = 42. Very close to 41 so I'll try adjacent bases

Base 9: 14*3 = 43. Moving away from 41, so try the other side

Base 11: 14*3 = 41. There it is. The base sought is **base 11**.