1693 ÷ 3 = 564 R1
Alright, let's work through the division of 1693 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 (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 2:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 15 from 16 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 3

Step 3:
3 goes into 19 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 56
Subtract 18 from 19 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: 564
Subtract 12 from 13 to get 1.

The final result is 564 with a remainder of 1.