13016 ÷ 7 = 1859 R3
Alright, let's work through the division of 13016 by 7 step by step.

Step 1:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 2:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 13 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 7

Step 3:
7 goes into 60 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 18
Subtract 56 from 60 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 7

Step 4:
7 goes into 41 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 185
Subtract 35 from 41 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 5:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 1859
Subtract 63 from 66 to get 3.

The final result is 1859 with a remainder of 3.