Notice that 312 is divisible by 3, while 427 is not.


Every third number from 312 to 427 is divisible by 3.



    (The precise meaning of the previous phrase is that among every group of three consecutive integer numbers 

      exactly one is divisible by 3).



The number of consecutive disjoint triples of integer numbers from 312 to 427 is the integer part of the 

number   = 38.67, i.e. 38.


It gives you the 


ANSWER.  There are 38 integer numbers between 312 and 427, divisible by 3.


CHECK.  (312-1) + 3*38 = 425.