87814 ÷ 6 = 14635 R4
Alright, let's work through the division of 87814 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 (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 2:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 24 from 27 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 3:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 146
Subtract 36 from 38 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 4:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 1463
Subtract 18 from 21 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 6

Step 5:
6 goes into 34 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 14635
Subtract 30 from 34 to get 4.

The final result is 14635 with a remainder of 4.