19037 ÷ 8 = 2379 R5
Alright, let's work through the division of 19037 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 (9) of the dividend behind the 1 and repeat the process: 19 / 8

Step 2:
8 goes into 19 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 16 from 19 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 8

Step 3:
8 goes into 30 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 23
Subtract 24 from 30 to get 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 8

Step 4:
8 goes into 63 7 times with a remainder of 7.
Write down 7 as next digit of of the result. 
Result so far: 237
Subtract 56 from 63 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 8

Step 5:
8 goes into 77 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 2379
Subtract 72 from 77 to get 5.

The final result is 2379 with a remainder of 5.