17914 ÷ 8 = 2239 R2
Alright, let's work through the division of 17914 by 8 step by step.

Step 1:
8 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 8

Step 2:
8 goes into 17 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 16 from 17 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 8

Step 3:
8 goes into 19 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 22
Subtract 16 from 19 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: 223
Subtract 24 from 31 to get 7.
Bring next digit (4) of the dividend behind the 7 and repeat the process: 74 / 8

Step 5:
8 goes into 74 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 2239
Subtract 72 from 74 to get 2.

The final result is 2239 with a remainder of 2.