21415 ÷ 6 = 3569 R1
We're going to perform division on 21415 with 6 as the divisor.

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 (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 2:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 18 from 21 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: 35
Subtract 30 from 34 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 6

Step 4:
6 goes into 41 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 356
Subtract 36 from 41 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 6

Step 5:
6 goes into 55 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 3569
Subtract 54 from 55 to get 1.

The final result is 3569 with a remainder of 1.