We try:

1122 ÷ 11 = 102

111222 ÷ 111 = 1002

11112222 ÷ 1111 = 10002

So: N ÷ A = B where N=111...1222...2 (1999 digits of 1 followed by 1999 digits of 2), A is 1999 digits of 1 and B = 1000...02 has 1998 digits of 0.

We also see:

102 ÷ 2 = 51

1002 ÷ 2 = 501

10002 ÷ 2 = 5001

So B ÷ 2 = C where C = 5000...01 with 1997 digits of 0.

And

51 ÷ 3 = 17

501 ÷ 3 = 167

5001 ÷ 3 = 1667

So C ÷ 3 = D where D = 1666...67 with 1997 digits of 6.

Ans finally N = A ⋅ B C ⋅ D = 111…1 ⋅ 2 3 ⋅ ⋅ 1666…67