86819 ÷ 7 = 12402 R5
Alright, let's work through the division of 86819 by 7 step by step.

Step 1:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 8 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 7

Step 2:
7 goes into 16 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 14 from 16 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 7

Step 3:
7 goes into 28 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 124
Subtract 28 from 28 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 7

Step 4:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 1240
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 7

Step 5:
7 goes into 19 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 12402
Subtract 14 from 19 to get 5.

The final result is 12402 with a remainder of 5.