71501 ÷ 7 = 10214 R3
Alright, let's work through the division of 71501 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 (0) of the dividend behind the 1 and repeat the process: 10 / 7

Step 4:
7 goes into 10 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1021
Subtract 7 from 10 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 7

Step 5:
7 goes into 31 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 10214
Subtract 28 from 31 to get 3.

The final result is 10214 with a remainder of 3.