13306 ÷ 3 = 4435 R1
Alright, let's work through the division of 13306 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 (3) of the dividend behind the 1 and repeat the process: 13 / 3

Step 2:
3 goes into 13 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 12 from 13 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: 44
Subtract 12 from 13 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 3

Step 4:
3 goes into 10 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 443
Subtract 9 from 10 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 5:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 4435
Subtract 15 from 16 to get 1.

The final result is 4435 with a remainder of 1.