65971 ÷ 8 = 8246 R3
Alright, let's work through the division of 65971 by 8 step by step.

Step 1:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 8

Step 2:
8 goes into 65 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 65 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: 82
Subtract 16 from 19 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 8

Step 4:
8 goes into 37 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 824
Subtract 32 from 37 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 8

Step 5:
8 goes into 51 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 8246
Subtract 48 from 51 to get 3.

The final result is 8246 with a remainder of 3.