41340 ÷ 4 = 10335 R0
Alright, let's work through the division of 41340 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 (3) of the dividend behind the 1 and repeat the process: 13 / 4

Step 3:
4 goes into 13 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 103
Subtract 12 from 13 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 4

Step 4:
4 goes into 14 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 1033
Subtract 12 from 14 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 4

Step 5:
4 goes into 20 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 10335
Subtract 20 from 20 to get 0.

The final result is 10335 with a remainder of 0.