71742 ÷ 8 = 8967 R6
Alright, let's work through the division of 71742 by 8 step by step.

Step 1:
8 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 7 to get 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 8

Step 2:
8 goes into 71 8 times with a remainder of 7.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 71 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 8

Step 3:
8 goes into 77 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 89
Subtract 72 from 77 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 8

Step 4:
8 goes into 54 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 896
Subtract 48 from 54 to get 6.
Bring next digit (2) of the dividend behind the 6 and repeat the process: 62 / 8

Step 5:
8 goes into 62 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 8967
Subtract 56 from 62 to get 6.

The final result is 8967 with a remainder of 6.