72021 ÷ 6 = 12003 R3
Alright, let's work through the division of 72021 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 6

Step 2:
6 goes into 12 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 12 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 6

Step 3:
6 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 120
Subtract 0 from 0 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 6

Step 4:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 1200
Subtract 0 from 2 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: 12003
Subtract 18 from 21 to get 3.

The final result is 12003 with a remainder of 3.