13019 ÷ 8 = 1627 R3
Alright, let's work through the division of 13019 by 8 step by step.

Step 1:
8 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 / 8

Step 2:
8 goes into 13 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 13 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 8

Step 3:
8 goes into 50 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 48 from 50 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 8

Step 4:
8 goes into 21 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 162
Subtract 16 from 21 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 8

Step 5:
8 goes into 59 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 1627
Subtract 56 from 59 to get 3.

The final result is 1627 with a remainder of 3.