10365 ÷ 3 = 3455 R0
Alright, let's work through the division of 10365 by 3 step by step.

Step 1:
3 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 3

Step 2:
3 goes into 10 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 9 from 10 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 3

Step 3:
3 goes into 13 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 34
Subtract 12 from 13 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 4:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 345
Subtract 15 from 16 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Step 5:
3 goes into 15 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 3455
Subtract 15 from 15 to get 0.

The final result is 3455 with a remainder of 0.