89781 ÷ 6 = 14963 R3
Alright, let's work through the division of 89781 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 (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 3:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 149
Subtract 54 from 57 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 4:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 1496
Subtract 36 from 38 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 5:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 14963
Subtract 18 from 21 to get 3.

The final result is 14963 with a remainder of 3.