86721 ÷ 4 = 21680 R1
Alright, let's work through the division of 86721 by 4 step by step.

Step 1:
4 goes into 8 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 8 from 8 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 2:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 21
Subtract 4 from 6 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 4

Step 3:
4 goes into 27 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 216
Subtract 24 from 27 to get 3.
Bring next digit (2) of the dividend behind the 3 and repeat the process: 32 / 4

Step 4:
4 goes into 32 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 2168
Subtract 32 from 32 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 4

Step 5:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 21680
Subtract 0 from 1 to get 1.

The final result is 21680 with a remainder of 1.