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.