15339 ÷ 8 = 1917 R3
Alright, let's work through the division of 15339 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 (5) of the dividend behind the 1 and repeat the process: 15 / 8

Step 2:
8 goes into 15 1 times with a remainder of 7.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 15 to get 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 8

Step 3:
8 goes into 73 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 72 from 73 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 8

Step 4:
8 goes into 13 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 191
Subtract 8 from 13 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: 1917
Subtract 56 from 59 to get 3.

The final result is 1917 with a remainder of 3.