34099 ÷ 7 = 4871 R2
Alright, let's work through the division of 34099 by 7 step by step.

Step 1:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 7

Step 2:
7 goes into 34 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 28 from 34 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: 48
Subtract 56 from 60 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 7

Step 4:
7 goes into 49 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 487
Subtract 49 from 49 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 7

Step 5:
7 goes into 9 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 4871
Subtract 7 from 9 to get 2.

The final result is 4871 with a remainder of 2.