71745 ÷ 7 = 10249 R2
Alright, let's work through the division of 71745 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 (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 3:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 14 from 17 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 7

Step 4:
7 goes into 34 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 1024
Subtract 28 from 34 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 7

Step 5:
7 goes into 65 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 10249
Subtract 63 from 65 to get 2.

The final result is 10249 with a remainder of 2.