10355 ÷ 3 = 3451 R2
Alright, let's work through the division of 10355 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 (5) of the dividend behind the 1 and repeat the process: 15 / 3

Step 4:
3 goes into 15 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 345
Subtract 15 from 15 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Step 5:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 3451
Subtract 3 from 5 to get 2.

The final result is 3451 with a remainder of 2.