96349 ÷ 6 = 16058 R1
Alright, let's work through the division of 96349 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 (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 3:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 160
Subtract 0 from 3 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 6

Step 4:
6 goes into 34 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 1605
Subtract 30 from 34 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 6

Step 5:
6 goes into 49 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 16058
Subtract 48 from 49 to get 1.

The final result is 16058 with a remainder of 1.