41205 ÷ 4 = 10301 R1
Alright, let's work through the division of 41205 by 4 step by step.

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

Step 2:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 4

Step 3:
4 goes into 12 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 103
Subtract 12 from 12 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 4

Step 4:
4 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 1030
Subtract 0 from 0 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 4

Step 5:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 10301
Subtract 4 from 5 to get 1.

The final result is 10301 with a remainder of 1.