6097 ÷ 3 = 2032 R1
Alright, let's work through the division of 6097 by 3 step by step.

Step 1:
3 goes into 6 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 6 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 3

Step 2:
3 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 20
Subtract 0 from 0 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 3

Step 3:
3 goes into 9 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 203
Subtract 9 from 9 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: 2032
Subtract 6 from 7 to get 1.

The final result is 2032 with a remainder of 1.