27421 ÷ 6 = 4570 R1
Alright, let's work through the division of 27421 by 6 step by step.

Step 1:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 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: 4
Subtract 24 from 27 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 6

Step 3:
6 goes into 34 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 45
Subtract 30 from 34 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 6

Step 4:
6 goes into 42 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 457
Subtract 42 from 42 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 5:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 4570
Subtract 0 from 1 to get 1.

The final result is 4570 with a remainder of 1.