The first batch, the second batch and the third batch processed by the apprentice are A, B and C respectively.
na+7=2 100
nb+6= 1800
nc+ 13= 1600
n = 2093/a = 1794/b = 1587/c
Decomposition factor:
2093=23* 13*7
1794=23* 13*3*2
1587=23*23*3
Only common factor 23 and 1 (irrelevant, omitted)
So the number of disciples =23- 1=22.