10313 ÷ 3 = 3437 R2
Alright, let's work through the division of 10313 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 (1) of the dividend behind the 1 and repeat the process: 11 / 3

Step 4:
3 goes into 11 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 343
Subtract 9 from 11 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Step 5:
3 goes into 23 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 3437
Subtract 21 from 23 to get 2.

The final result is 3437 with a remainder of 2.