3337 ÷ 3 = 1112 R1
Alright, let's work through the division of 3337 by 3 step by step.

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

Step 2:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 3 from 3 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 3

Step 3:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 111
Subtract 3 from 3 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 3

Step 4:
3 goes into 7 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 1112
Subtract 6 from 7 to get 1.

The final result is 1112 with a remainder of 1.