9697 ÷ 6 = 1616 R1
Alright, let's work through the division of 9697 by 6 step by step.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 2:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 36 from 36 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 6

Step 3:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 161
Subtract 6 from 9 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 4:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 1616
Subtract 36 from 37 to get 1.

The final result is 1616 with a remainder of 1.