21318 ÷ 8 = 2664 R6
Alright, let's work through the division of 21318 by 8 step by step.

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 (3) of the dividend behind the 5 and repeat the process: 53 / 8

Step 3:
8 goes into 53 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 26
Subtract 48 from 53 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 8

Step 4:
8 goes into 51 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 266
Subtract 48 from 51 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 8

Step 5:
8 goes into 38 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 2664
Subtract 32 from 38 to get 6.

The final result is 2664 with a remainder of 6.