15038 ÷ 6 = 2506 R2
Alright, let's work through the division of 15038 by 6 step by step.

Step 1:
6 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 (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 2:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 12 from 15 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 6

Step 3:
6 goes into 30 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 25
Subtract 30 from 30 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 6

Step 4:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 250
Subtract 0 from 3 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 5:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 2506
Subtract 36 from 38 to get 2.

The final result is 2506 with a remainder of 2.