2053 ÷ 3 = 684 R1
Alright, let's work through the division of 2053 by 3 step by step.

Step 1:
3 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 3

Step 2:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 18 from 20 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 3

Step 3:
3 goes into 25 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 68
Subtract 24 from 25 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 3

Step 4:
3 goes into 13 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 684
Subtract 12 from 13 to get 1.

The final result is 684 with a remainder of 1.