21111 ÷ 8 = 2638 R7
We're going to perform division on 21111 with 8 as the divisor.

Step 1:
8 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 / 8

Step 2:
8 goes into 21 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 16 from 21 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 8

Step 3:
8 goes into 51 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 48 from 51 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 8

Step 4:
8 goes into 31 3 times with a remainder of 7.
Write down 3 as next digit of of the result. 
Result so far: 263
Subtract 24 from 31 to get 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 8

Step 5:
8 goes into 71 8 times with a remainder of 7.
Write down 8 as next digit of of the result. 
Result so far: 2638
Subtract 64 from 71 to get 7.

The final result is 2638 with a remainder of 7.