43559 ÷ 2 = 21779 R1
Alright, let's work through the division of 43559 by 2 step by step.

Step 1:
2 goes into 4 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 4 from 4 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 2

Step 2:
2 goes into 3 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 21
Subtract 2 from 3 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 2

Step 3:
2 goes into 15 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 217
Subtract 14 from 15 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 2

Step 4:
2 goes into 15 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 2177
Subtract 14 from 15 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 5:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 21779
Subtract 18 from 19 to get 1.

The final result is 21779 with a remainder of 1.