71565 ÷ 7 = 10223 R4
Alright, let's work through the division of 71565 by 7 step by step.

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

Step 2:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 7

Step 3:
7 goes into 15 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 14 from 15 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 7

Step 4:
7 goes into 16 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 1022
Subtract 14 from 16 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 7

Step 5:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 10223
Subtract 21 from 25 to get 4.

The final result is 10223 with a remainder of 4.