Ways in which 38 can be divided into 3 positive parts such that the first is divisible by 8, the second by 7 and the third part by 3? I am stuck with the question, i have tried a couple of random approaches but none of them is correct. The answer is 2. Please help if you know how to solve this question.

Using the fact that second and third part should both be either even or odd, number of possibilities are reduced very much. For first part =8, 21,  9 are the solution.
For first part= 16, 7, 15 are the solution
