89638 ÷ 6 = 14939 R4
Alright, let's work through the division of 89638 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

Step 2:
6 goes into 29 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 24 from 29 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 3:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 149
Subtract 54 from 56 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 4:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 1493
Subtract 18 from 23 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 6

Step 5:
6 goes into 58 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 14939
Subtract 54 from 58 to get 4.

The final result is 14939 with a remainder of 4.